Finance and insurance

Educational objectives

The course provides students with advanced mathematical training, which is essential for the understanding and implementation of quantitative models used in economic analysis, corporate decision-making processes, and specific applications in finance. The course develops core topics in linear algebra, functions of several variables, unconstrained and constrained optimization techniques, and ordinary differential equations, offering an integrated framework that combines theoretical foundations with operational tools and constitutes the methodological basis for the quantitative courses of the Master’s degree programme. At the end of the course, students will know and understand the tools of advanced mathematics required to address complex quantitative models, including those underlying the analysis of stochastic processes and the fundamental techniques for the valuation of derivative instruments. They will develop proficiency in the study of quadratic forms, matrix diagonalization, multivariate function analysis, and solution methods for differential equations and systems, and will be able to apply these tools to analyze, interpret, and solve problems in economic and financial modelling. Students will further develop the ability to formulate rigorous quantitative assessments and to use mathematical techniques that are functional to the construction and understanding of fair valuation models for financial instruments. They will develop the capacity to formulate independent judgments on the results obtained, compare alternative solutions, and evaluate the consistency of the assumptions underlying the models employed. Students will also be able to communicate methods, arguments, and results clearly and rigorously, using mathematical formalism appropriately. Finally, they will acquire appropriate learning skills that will enable them to independently deepen more advanced topics and to confidently tackle subsequent quantitative courses in the Master’s degree programme.

Educational objectives

Learning Objectives
The course aims to provide students with a rigorous and in-depth knowledge of the foundations of modern probability theory and of the main discrete- and continuous-time stochastic processes, such as random walks, Markov chains, and Brownian motion. The course introduces the fundamental concepts of probability through a rigorous definition of the main terms and structures, accompanied by the discussion and proof of the most relevant theoretical results. It combines theoretical rigor with practical applications, fostering the development of modelling and analytical skills for the study of complex economic and financial phenomena. At the end of the course, students will acquire both theoretical and operational knowledge enabling them to understand and interpret probabilistic models and stochastic processes. They will be able to apply this knowledge to solve quantitative problems, formalize appropriate models, and interpret their results. Students will develop the ability to formulate independent judgments on the models adopted, to communicate concepts and results clearly and rigorously, both orally and in writing, and to independently deepen advanced topics in probability and stochastic processes, consolidating a critical and analytical approach. The course provides the essential methodological foundation for successfully undertaking advanced courses such as Quantitative Finance, Methods and Models for Finance, Actuarial Mathematics for Private Insurance, Risk Theory, and Time Series Analysis, and offers tools that are also relevant for postgraduate education and professional applications in quantitative and financial fields.

Educational objectives

Learning Objectives
The course aims to provide students with an in-depth knowledge of the main approaches used internationally by financial analysts, investment and merchant banks, and consulting firms for the valuation of companies, acquisitions, initial public offerings, and business combination transactions. The course seeks to develop analytical sensitivity to these topics, grounded in a solid theoretical and methodological framework. At the end of the course, students will acquire both theoretical and operational knowledge of the main business valuation tools and will be able to apply them to practical cases. They will develop the ability to critically analyze alternative approaches, interpret quantitative and qualitative results, and clearly communicate valuation criteria and choices, both orally and in writing. In addition, by the end of the course, students will acquire the skills necessary to independently deepen advanced methodologies in corporate finance and business valuation. The course also provides methodological and practical preparation that is useful for professional qualification examinations and for consultancy activities in the field of corporate finance.

Educational objectives

The course is part of the additional training activities and aims to provide students with the foundations for using the R software for the numerical computation of integrals, with particular emphasis on the Monte Carlo method, and for the simulation of random variables and stochastic processes. The course enables students to replicate, through simulation, the main theoretical results of probability theory, such as the law of large numbers and the central limit theorem, and to simulate stochastic processes in both discrete time (random walks and Markov chains) and continuous time (Poisson process). At the end of the course, students will have strengthened their theoretical background and acquired operational knowledge in the use of simulation tools for probabilistic and stochastic processes. They will be able to apply these tools to analyze economic and financial phenomena, interpret their dynamics, and identify their main characteristics. Students will develop the ability to formulate independent judgments regarding the choice of models and simulation methods, to clearly communicate concepts, procedures, and results, both orally and in writing, and to independently deepen the computational and mathematical-statistical skills acquired. The course provides an additional methodological competence for successfully undertaking advanced quantitative courses, such as Time Series Analysis, Quantitative Finance, and other numerically oriented courses.

Educational objectives

The course in Time Series Analysis aims to provide students with the methodological and operational skills necessary for the analysis of economic and financial time series, with particular focus on the construction, estimation, and evaluation of statistical and econometric models. The course integrates graphical analysis with a quantitative and methodological approach, enabling students to tackle real empirical problems in a rigorous and structured manner. The use of the statistical software R is an integral part of the course and is intended both for the analysis of real data and for exploring the properties of theoretical models and their empirical applicability. At the end of the course, students will have acquired a solid sensitivity to empirical data analysis, will be able to select the most appropriate model to describe economic and financial phenomena, define analysis strategies consistent with the problem under investigation, and critically interpret the results obtained. The course also fosters the development of critical thinking through the analysis of real cases and the completion of a research project, promoting the ability to communicate clearly and rigorously the methodologies used and the results of quantitative analyses. The skills acquired provide an essential foundation for independently exploring advanced models and for pursuing further studies in quantitative and economic-financial fields.

Educational objectives

The course provides students with the theoretical and methodological tools required to understand the evolution of financial systems in the major advanced economies, the role of financial intermediaries, and the interaction between economic agents and markets. The course enables students to analyze and compare business models and operational structures of international financial systems, interpreting their dynamics and potential developments. At the end of the course, students will acquire solid theoretical knowledge of the main international financial systems and intermediation models. They will be able to apply this knowledge to comparative analyses and critical evaluations of financial systems, develop independent judgement in interpreting the operational and methodological choices of financial intermediaries, and independently deepen the analysis of interactions between economic needs and the performance of financial markets. The course provides an essential foundation for successfully undertaking advanced courses in international finance, market regulation, risk management, and investment strategies, as well as for professional careers in the global financial sector.

Educational objectives

The course in Quantitative Finance aims to provide students with in-depth knowledge of numerical methodologies for the valuation of derivative financial instruments, where the underlying assets are modeled using discrete-time and continuous-time stochastic processes. The course gradually introduces the transition from discrete models to continuous diffusion models, with particular reference to the Black–Scholes–Merton framework, and addresses the main techniques for pricing and hedging derivatives. The course combines theoretical analysis of mathematical finance models with the computational implementation of valuation and hedging methodologies using MATLAB, enabling students to translate theoretical models into operational tools. At the end of the course, students will be able to understand, apply, and compare different numerical methodologies for the valuation of financial instruments, identifying the most suitable solutions according to the economic and financial context. The course provides an advanced methodological foundation for quantitative analysis of financial markets and constitutes a key reference for further studies in quantitative finance, in particular for courses such as Methods and Models for Finance and Financial Optimization, as well as for professional applications requiring modeling and numerical computation skills.

Educational objectives

The course aims to provide students with the advanced mathematical tools necessary to describe and analyze the main continuous-time models in quantitative finance used for the valuation of derivative securities in financial markets. The course deepens the foundations of stochastic calculus and the modeling of random processes relevant to finance, with particular reference to the term structure of interest rates and the valuation of derivatives on stocks and indices. The course integrates theoretical model analysis with their application to concrete economic and financial problems, enabling students to consistently move from mathematical formulation to fair valuation of financial instruments. At the end of the course, students will be able to select and apply the most appropriate models according to the market context, critically interpret the results obtained, and communicate methodologies and solutions rigorously. The course constitutes a fundamental component of advanced quantitative training and provides the methodological basis for access to postgraduate research or professional activities with a high quantitative-financial content.

Educational objectives

The course provides students with the theoretical and practical knowledge necessary to understand, assess, and manage financial risks. In particular, it enables students to acquire the skills required for determining the fair value of financial instruments, constructing performance indicators (KPIs), and conducting quantitative and scenario
analyses in real market contexts. The course combines theoretical discussions with practical applications of methodologies widely used in financial practice, developing the ability to identify the most appropriate quantitative modelling to describe market phenomena and to translate theoretical principles into analytical and decision-support tools. The use of software for calculation, simulation, and visualization of results allows students to consolidate operational skills and critically interpret analysis outputs. Through the study of practical cases, students will develop autonomous judgment, problem-solving skills, and sensitivity to predictive logic in financial markets. The course also enhances communication skills, promoting the use of technical-financial language in both written and oral form, and consolidates a method for autonomous and critical learning, useful for addressing advanced topics in quantitative analysis and risk management, also in preparation for post-graduate specialization programs.

Educational objectives

The educational regulations 270 provide, within each Degree Program, a specific number of credits to be allocated to "student's elective activities." The number of credits provided for this course is 9. These activities consist of exams related to modules offered in the Master's Degree programs of the Faculty or other Faculties at Sapienza.

Educational objectives

The course aims to provide students with a comprehensive and systematic understanding of the legal rules governing the functioning of financial markets, in light of national and European regulations and the most recent regulatory interventions. The course examines the complex system of rules and institutions that govern financial instruments, intermediaries, markets, and issuers, with particular attention to the role played by supervisory authorities, especially CONSOB and the Bank of Italy, in regulating, monitoring, and protecting the market and investors. At the end of the course, students will have acquired solid knowledge of the financial market regulatory framework and will be able to interpret and critically apply the main legal and regulatory sources, including provisions and pronouncements of the supervisory authorities. They will develop the ability to analyze the legal mechanisms underlying the operation of investment services and the governance of listed companies, formulate independent assessments of regulatory choices, and communicate their knowledge clearly and rigorously. The course also provides the methodological tools necessary for continuous updating of legal expertise in a constantly evolving regulatory context, being relevant both for further academic study and for professional careers in finance, regulation, and advisory services.

Educational objectives

The career-oriented training activities aim to enhance students’ transversal, practical, and professional skills, facilitating the transition into complex and dynamic work environments. These activities include participation in seminars, workshops, and online certification programs, organized in collaboration with companies and relevant institutions. The objective is to enrich students’ professional profiles by developing complementary skills, improving adaptability, productivity, and problem-solving abilities in financial, insurance, and technological fields. Practical and collaborative experiences are designed to strengthen independent judgment, critical thinking, analytical and communication skills, providing tools to define and pursue personal and professional goals. At the end of the program, students will be able to apply the transversal skills acquired, interact effectively with professionals and experts in the field, understand the dynamics of the labor market and research activities, and leverage their preparation in both professional and academic contexts. The study program also promotes internships with partner companies and institutions and, subject to authorization, may recognize participation in scientific conferences as an integral part of the training path.

Educational objectives

The final assessment of the master's degree program consists of the preparation and discussion of a thesis that demonstrates the student’s acquisition of advanced knowledge and specialized skills in quantitative models, computational techniques, and their application to financial, insurance, and risk management problems. The thesis represents an opportunity for methodological and experimental in-depth study, in which the student integrates knowledge acquired from different courses, engages with the scientific literature, and produces an original contribution on the chosen topic. Students will develop the ability to analyze complex phenomena, select and apply the most appropriate quantitative model, collect and process data, and interpret market and risk scenarios using digital tools such as Excel, dashboards, simulators, and dedicated software. The thesis also fosters collaborative skills through interactions with supervisors and peers and strengthens the ability to communicate analysis results clearly, concisely, and technically, with particular attention to presenting and justifying investment, hedging, and risk management strategies. Upon completion, students will be able to independently update their quantitative and regulatory skills in line with market developments and risk management techniques. The thesis certifies scientific maturity and critical autonomy necessary for pursuing post-graduate specialization paths, such as second-level master programs and PhD studies, and provides solid preparation for professional certification exams, including the actuarial profession, or for entering complex financial and insurance work environments.

Specific Learning Outcomes (Dublin Descriptors)
Knowledge and Understanding. The thesis enables students to consolidate the knowledge acquired in the various master’s courses, integrating theoretical, quantitative, and methodological skills. Students will be able to conduct in-depth research on a topic of interest, analyze the scientific literature, compare different approaches, and recognize the connections between theoretical and applied contributions.
Applying Knowledge and Understanding. The thesis allows students to apply quantitative models and theoretical-methodological tools to real-world problems in financial, insurance, and pension contexts. Students will be able to formalize the phenomena studied, collect and process data, use specialized software and digital tools, and propose original and effective solutions to the problems analyzed.
Making Judgements. Through the thesis, students acquire the ability to critically evaluate complex phenomena and select the most appropriate models to represent them. They will be able to interpret quantitative and qualitative results, formulate well-grounded conclusions, and suggest applicable strategies consistent with the real-world context studied.
Communication Skills. Writing and defending the thesis develops both written and oral communication skills, enabling students to organize a research project clearly and coherently, explain objectives, methodology, and results, and justify their choices. Students will be able to present the thesis content to both specialized and non-specialized audiences, using correct and context-appropriate technical language.
Learning Skills. The thesis certifies an advanced level of education, providing students with methodology, critical autonomy, and continuous learning skills. Upon completion, students will be able to explore new research topics, pursue post-graduate specialization programs such as master’s degrees or PhDs, and enter professional environments with solid competencies in finance, insurance, and actuarial fields.

Educational objectives

The course provides students with advanced mathematical training, which is essential for the understanding and implementation of quantitative models used in economic analysis, corporate decision-making processes, and specific applications in finance. The course develops core topics in linear algebra, functions of several variables, unconstrained and constrained optimization techniques, and ordinary differential equations, offering an integrated framework that combines theoretical foundations with operational tools and constitutes the methodological basis for the quantitative courses of the Master’s degree programme. At the end of the course, students will know and understand the tools of advanced mathematics required to address complex quantitative models, including those underlying the analysis of stochastic processes and the fundamental techniques for the valuation of derivative instruments. They will develop proficiency in the study of quadratic forms, matrix diagonalization, multivariate function analysis, and solution methods for differential equations and systems, and will be able to apply these tools to analyze, interpret, and solve problems in economic and financial modelling. Students will further develop the ability to formulate rigorous quantitative assessments and to use mathematical techniques that are functional to the construction and understanding of fair valuation models for financial instruments. They will develop the capacity to formulate independent judgments on the results obtained, compare alternative solutions, and evaluate the consistency of the assumptions underlying the models employed. Students will also be able to communicate methods, arguments, and results clearly and rigorously, using mathematical formalism appropriately. Finally, they will acquire appropriate learning skills that will enable them to independently deepen more advanced topics and to confidently tackle subsequent quantitative courses in the Master’s degree programme.

Educational objectives

Learning Objectives
The course aims to provide students with a rigorous and in-depth knowledge of the foundations of modern probability theory and of the main discrete- and continuous-time stochastic processes, such as random walks, Markov chains, and Brownian motion. The course introduces the fundamental concepts of probability through a rigorous definition of the main terms and structures, accompanied by the discussion and proof of the most relevant theoretical results. It combines theoretical rigor with practical applications, fostering the development of modelling and analytical skills for the study of complex economic and financial phenomena. At the end of the course, students will acquire both theoretical and operational knowledge enabling them to understand and interpret probabilistic models and stochastic processes. They will be able to apply this knowledge to solve quantitative problems, formalize appropriate models, and interpret their results. Students will develop the ability to formulate independent judgments on the models adopted, to communicate concepts and results clearly and rigorously, both orally and in writing, and to independently deepen advanced topics in probability and stochastic processes, consolidating a critical and analytical approach. The course provides the essential methodological foundation for successfully undertaking advanced courses such as Quantitative Finance, Methods and Models for Finance, Actuarial Mathematics for Private Insurance, Risk Theory, and Time Series Analysis, and offers tools that are also relevant for postgraduate education and professional applications in quantitative and financial fields.

Educational objectives

Learning Objectives
The course aims to provide students with an in-depth knowledge of the main approaches used internationally by financial analysts, investment and merchant banks, and consulting firms for the valuation of companies, acquisitions, initial public offerings, and business combination transactions. The course seeks to develop analytical sensitivity to these topics, grounded in a solid theoretical and methodological framework. At the end of the course, students will acquire both theoretical and operational knowledge of the main business valuation tools and will be able to apply them to practical cases. They will develop the ability to critically analyze alternative approaches, interpret quantitative and qualitative results, and clearly communicate valuation criteria and choices, both orally and in writing. In addition, by the end of the course, students will acquire the skills necessary to independently deepen advanced methodologies in corporate finance and business valuation. The course also provides methodological and practical preparation that is useful for professional qualification examinations and for consultancy activities in the field of corporate finance.

Educational objectives

The course is part of the additional training activities and aims to provide students with the foundations for using the R software for the numerical computation of integrals, with particular emphasis on the Monte Carlo method, and for the simulation of random variables and stochastic processes. The course enables students to replicate, through simulation, the main theoretical results of probability theory, such as the law of large numbers and the central limit theorem, and to simulate stochastic processes in both discrete time (random walks and Markov chains) and continuous time (Poisson process). At the end of the course, students will have strengthened their theoretical background and acquired operational knowledge in the use of simulation tools for probabilistic and stochastic processes. They will be able to apply these tools to analyze economic and financial phenomena, interpret their dynamics, and identify their main characteristics. Students will develop the ability to formulate independent judgments regarding the choice of models and simulation methods, to clearly communicate concepts, procedures, and results, both orally and in writing, and to independently deepen the computational and mathematical-statistical skills acquired. The course provides an additional methodological competence for successfully undertaking advanced quantitative courses, such as Time Series Analysis, Quantitative Finance, and other numerically oriented courses.

Educational objectives

The course provides students with the theoretical and methodological tools required to understand the evolution of financial systems in the major advanced economies, the role of financial intermediaries, and the interaction between economic agents and markets. The course enables students to analyze and compare business models and operational structures of international financial systems, interpreting their dynamics and potential developments. At the end of the course, students will acquire solid theoretical knowledge of the main international financial systems and intermediation models. They will be able to apply this knowledge to comparative analyses and critical evaluations of financial systems, develop independent judgement in interpreting the operational and methodological choices of financial intermediaries, and independently deepen the analysis of interactions between economic needs and the performance of financial markets. The course provides an essential foundation for successfully undertaking advanced courses in international finance, market regulation, risk management, and investment strategies, as well as for professional careers in the global financial sector.

Educational objectives

The course aims to introduce students to the main methods and models of actuarial mathematics and to illustrate their application in the valuation and management of life and non-life insurance contracts. The course deepens both theoretical foundations and practical aspects, potentially through computational techniques, for the determination of premiums and reserves, as well as in pricing, hedging, diversification, and portfolio profit formation. By the end of the course, students will acquire a structured understanding of actuarial models for private insurance and the underlying mathematical-probabilistic tools. They will be able to apply these models to the valuation of traditional and flexible benefit insurance contracts, develop independent judgment regarding technical assumptions and modeling choices, communicate actuarial analysis results rigorously, and independently deepen advanced methodologies for risk measurement and management. The course provides an essential methodological foundation for subsequent actuarial courses, as well as for professional applications in insurance, pension, and risk management fields.

Educational objectives

The course aims to introduce students to the main probabilistic models and quantitative techniques used in insurance risk management, with particular focus on non-life insurance companies. The course covers classical risk models, risk measures, solvency issues, and the main forms of reinsurance, highlighting their role in the financial stability of insurance companies. By the end of the course, students will acquire a structured understanding of insurance risk models and probabilistic tools for solvency assessment. They will be able to apply these models to analyze the probability of ruin and evaluate the effects of reinsurance, develop independent judgment in selecting risk measures and hedging strategies, communicate quantitative analysis results rigorously, and independently deepen advanced topics in insurance risk management. Together with Actuarial Mathematics for Private Insurance, the course provides an essential methodological foundation for subsequent actuarial courses, as well as for professional applications in insurance, pensions, and risk management.

Specific Learning Outcomes (Dublin Descriptors)
Knowledge and Understanding. By the end of the course, students will acquire knowledge of the main models in insurance risk theory, with particular reference to the Cramér–Lundberg process. They will understand the probabilistic techniques used for assessing an insurer’s solvency, the main risk measures, and reinsurance forms adopted in practice, as well as their effects on the company’s risk profile.
Applying Knowledge and Understanding. At the end of the course, students will be able to apply risk models to evaluate the probability of ruin for an insurance company in contexts of comparable complexity to those addressed in the course. They will analyze the impact of different reinsurance arrangements on the risk process and risk measures, as well as determine optimal reinsurance levels in standard applied contexts.
Making Judgements. Upon successful completion of the course, students will develop the ability to critically evaluate the adequacy of adopted risk models and underlying assumptions. They will be able to compare alternative risk management strategies, interpret results, and discuss the limitations of the approximations used, taking into account the operational needs of an insurance company.
Communication Skills. Students will be able to clearly and rigorously describe and discuss insurance risk models, analytical methodologies, and results. They will communicate their assessments both orally and in written reports, using language appropriate to the actuarial and insurance context.
Learning Skills. By the end of the course, students will have acquired the skills necessary to independently update and develop their knowledge in insurance risk management. They will be able to explore more advanced risk theory models and apply the learned tools to new professional and regulatory contexts within the insurance sector.

Educational objectives

The course aims to introduce students to the main probabilistic models and quantitative techniques used in insurance risk management, with particular focus on non-life insurance companies. The course covers classical risk models, risk measures, solvency issues, and the main forms of reinsurance, highlighting their role in the financial stability of insurance companies. By the end of the course, students will acquire a structured understanding of insurance risk models and probabilistic tools for solvency assessment. They will be able to apply these models to analyze the probability of ruin and evaluate the effects of reinsurance, develop independent judgment in selecting risk measures and hedging strategies, communicate quantitative analysis results rigorously, and independently deepen advanced topics in insurance risk management. Together with Actuarial Mathematics for Private Insurance, the course provides an essential methodological foundation for subsequent actuarial courses, as well as for professional applications in insurance, pensions, and risk management.

Specific Learning Outcomes (Dublin Descriptors)
Knowledge and Understanding. By the end of the course, students will acquire knowledge of the main models in insurance risk theory, with particular reference to the Cramér–Lundberg process. They will understand the probabilistic techniques used for assessing an insurer’s solvency, the main risk measures, and reinsurance forms adopted in practice, as well as their effects on the company’s risk profile.
Applying Knowledge and Understanding. At the end of the course, students will be able to apply risk models to evaluate the probability of ruin for an insurance company in contexts of comparable complexity to those addressed in the course. They will analyze the impact of different reinsurance arrangements on the risk process and risk measures, as well as determine optimal reinsurance levels in standard applied contexts.
Making Judgements. Upon successful completion of the course, students will develop the ability to critically evaluate the adequacy of adopted risk models and underlying assumptions. They will be able to compare alternative risk management strategies, interpret results, and discuss the limitations of the approximations used, taking into account the operational needs of an insurance company.
Communication Skills. Students will be able to clearly and rigorously describe and discuss insurance risk models, analytical methodologies, and results. They will communicate their assessments both orally and in written reports, using language appropriate to the actuarial and insurance context.
Learning Skills. By the end of the course, students will have acquired the skills necessary to independently update and develop their knowledge in insurance risk management. They will be able to explore more advanced risk theory models and apply the learned tools to new professional and regulatory contexts within the insurance sector.

Educational objectives

The course aims to introduce students to the main probabilistic models and quantitative techniques used in insurance risk management, with particular focus on non-life insurance companies. The course covers classical risk models, risk measures, solvency issues, and the main forms of reinsurance, highlighting their role in the financial stability of insurance companies. By the end of the course, students will acquire a structured understanding of insurance risk models and probabilistic tools for solvency assessment. They will be able to apply these models to analyze the probability of ruin and evaluate the effects of reinsurance, develop independent judgment in selecting risk measures and hedging strategies, communicate quantitative analysis results rigorously, and independently deepen advanced topics in insurance risk management. Together with Actuarial Mathematics for Private Insurance, the course provides an essential methodological foundation for subsequent actuarial courses, as well as for professional applications in insurance, pensions, and risk management.

Specific Learning Outcomes (Dublin Descriptors)
Knowledge and Understanding. By the end of the course, students will acquire knowledge of the main models in insurance risk theory, with particular reference to the Cramér–Lundberg process. They will understand the probabilistic techniques used for assessing an insurer’s solvency, the main risk measures, and reinsurance forms adopted in practice, as well as their effects on the company’s risk profile.
Applying Knowledge and Understanding. At the end of the course, students will be able to apply risk models to evaluate the probability of ruin for an insurance company in contexts of comparable complexity to those addressed in the course. They will analyze the impact of different reinsurance arrangements on the risk process and risk measures, as well as determine optimal reinsurance levels in standard applied contexts.
Making Judgements. Upon successful completion of the course, students will develop the ability to critically evaluate the adequacy of adopted risk models and underlying assumptions. They will be able to compare alternative risk management strategies, interpret results, and discuss the limitations of the approximations used, taking into account the operational needs of an insurance company.
Communication Skills. Students will be able to clearly and rigorously describe and discuss insurance risk models, analytical methodologies, and results. They will communicate their assessments both orally and in written reports, using language appropriate to the actuarial and insurance context.
Learning Skills. By the end of the course, students will have acquired the skills necessary to independently update and develop their knowledge in insurance risk management. They will be able to explore more advanced risk theory models and apply the learned tools to new professional and regulatory contexts within the insurance sector.

Educational objectives

The course aims to provide students with a comprehensive understanding of the fundamental principles of insurance law, with particular focus on insurance companies and insurance contracts. The course seeks to develop the ability to understand, interpret, and apply legal norms in the insurance context, promoting a critical and systematic approach to regulatory issues. By the end of the course, students will be able to correctly qualify facts to identify the applicable legal framework, analyze the rules and principles of insurance law, and communicate their interpretations and evaluations clearly and effectively. The course provides an essential foundation for further studies in insurance law and for professional or consulting activities in the insurance sector.

Educational objectives

The course addresses the calculation of premiums and reserves for next-generation life insurance products, considering both civil law and market-consistent perspectives, with particular focus on the solvency capital requirements associated with these products. The course enables students to use pricing and reserving models for revaluable contracts, as well as index-linked and unit-linked insurance products, applying both local accounting standards (Local GAAP) and international standards (IAS and Solvency II), following a Fair Value approach. By the end of the course, students will be able to independently apply quantitative models to calculate premiums, mathematical reserves, and solvency capital requirements. They will develop actuarial and financial awareness in evaluating innovative insurance contracts, acquire the ability to communicate technical concepts and results clearly, and be able to autonomously update themselves on regulatory sources and quantitative methodologies. The course also provides the specific preparation necessary to take the professional Actuary exam on the covered topics.

Educational objectives

The course aims to provide students with foundational knowledge and technical actuarial, financial, and demographic tools to analyze pension systems. Particular attention is given to comparing the Italian pension system, including both public mandatory and private components, with the Swedish system, considered one of the most technically advanced. The course enables students to understand the fundamentals of pension system design and management, including benefit calculation, financial sustainability, and the preparation of individual technical accounts. Students will also learn to assess the sustainability of partially funded contributory systems using the Theory of Logical Sustainability. By the end of the course, students will be able to analyze the sustainability of pension systems, apply actuarial and financial models to evaluate benefits and accounts, prepare clear and coherent technical reports, and develop autonomy in critically interpreting relevant regulations. The acquired skills also provide essential preparation for the professional Actuary exam and for the study of advanced pension topics.

Educational objectives

The educational regulations 270 provide, within each Degree Program, a specific number of credits to be allocated to "student's elective activities." The number of credits provided for this course is 9. These activities consist of exams related to modules offered in the Master's Degree programs of the Faculty or other Faculties at Sapienza.

Educational objectives

The career-oriented training activities aim to enhance students’ transversal, practical, and professional skills, facilitating the transition into complex and dynamic work environments. These activities include participation in seminars, workshops, and online certification programs, organized in collaboration with companies and relevant institutions. The objective is to enrich students’ professional profiles by developing complementary skills, improving adaptability, productivity, and problem-solving abilities in financial, insurance, and technological fields. Practical and collaborative experiences are designed to strengthen independent judgment, critical thinking, analytical and communication skills, providing tools to define and pursue personal and professional goals. At the end of the program, students will be able to apply the transversal skills acquired, interact effectively with professionals and experts in the field, understand the dynamics of the labor market and research activities, and leverage their preparation in both professional and academic contexts. The study program also promotes internships with partner companies and institutions and, subject to authorization, may recognize participation in scientific conferences as an integral part of the training path.

Educational objectives

The final assessment of the master's degree program consists of the preparation and discussion of a thesis that demonstrates the student’s acquisition of advanced knowledge and specialized skills in quantitative models, computational techniques, and their application to financial, insurance, and risk management problems. The thesis represents an opportunity for methodological and experimental in-depth study, in which the student integrates knowledge acquired from different courses, engages with the scientific literature, and produces an original contribution on the chosen topic. Students will develop the ability to analyze complex phenomena, select and apply the most appropriate quantitative model, collect and process data, and interpret market and risk scenarios using digital tools such as Excel, dashboards, simulators, and dedicated software. The thesis also fosters collaborative skills through interactions with supervisors and peers and strengthens the ability to communicate analysis results clearly, concisely, and technically, with particular attention to presenting and justifying investment, hedging, and risk management strategies. Upon completion, students will be able to independently update their quantitative and regulatory skills in line with market developments and risk management techniques. The thesis certifies scientific maturity and critical autonomy necessary for pursuing post-graduate specialization paths, such as second-level master programs and PhD studies, and provides solid preparation for professional certification exams, including the actuarial profession, or for entering complex financial and insurance work environments.

Specific Learning Outcomes (Dublin Descriptors)
Knowledge and Understanding. The thesis enables students to consolidate the knowledge acquired in the various master’s courses, integrating theoretical, quantitative, and methodological skills. Students will be able to conduct in-depth research on a topic of interest, analyze the scientific literature, compare different approaches, and recognize the connections between theoretical and applied contributions.
Applying Knowledge and Understanding. The thesis allows students to apply quantitative models and theoretical-methodological tools to real-world problems in financial, insurance, and pension contexts. Students will be able to formalize the phenomena studied, collect and process data, use specialized software and digital tools, and propose original and effective solutions to the problems analyzed.
Making Judgements. Through the thesis, students acquire the ability to critically evaluate complex phenomena and select the most appropriate models to represent them. They will be able to interpret quantitative and qualitative results, formulate well-grounded conclusions, and suggest applicable strategies consistent with the real-world context studied.
Communication Skills. Writing and defending the thesis develops both written and oral communication skills, enabling students to organize a research project clearly and coherently, explain objectives, methodology, and results, and justify their choices. Students will be able to present the thesis content to both specialized and non-specialized audiences, using correct and context-appropriate technical language.
Learning Skills. The thesis certifies an advanced level of education, providing students with methodology, critical autonomy, and continuous learning skills. Upon completion, students will be able to explore new research topics, pursue post-graduate specialization programs such as master’s degrees or PhDs, and enter professional environments with solid competencies in finance, insurance, and actuarial fields.

Educational objectives

The course aims to equip students with mathematical concepts and methods for addressing economic and financial problems. Topics include linear algebra, multivariable functions, continuous optimization methods, and techniques for solving differential equations. Special attention is given to the use of the term structure of interest rates for the valuation of financial cash flows. By the end of the course, students will understand the formal modeling of quantitative problems in economics and finance and possess the tools for their analytical solution. They will be able to evaluate real-world problems, identify the most appropriate model for each case, and interpret results correctly within the studied economic-financial context. Students will also be able to present quantitative analyses clearly and rigorously using formal mathematical language. Overall, they will have developed a critical study methodology and autonomous analytical skills, essential for successfully following subsequent quantitative courses in the Master’s program in Finance and Insurance (FinAss) and for preparing for advanced studies such as second-level master’s programs and PhD research in quantitative fields.

Educational objectives

The course provides students with theoretical and practical knowledge of probability calculus and stochastic processes, fundamental tools for analyzing and modeling economic and financial phenomena. Students will learn to formalize uncertainty, describe and interpret random phenomena through probabilistic models, and apply these models to analyze data variability, particularly related to risk in financial markets. By the end of the course, students will understand the main stochastic models for problems affected by uncertainty and will be able to perform quantitative assessments and predictions. They will be able to solve quantitative problems using analytical tools and select the most appropriate model to describe and study different random phenomena. Students will also be able to analyze time-evolving stochastic processes and interpret results critically, discussing their reliability and consistency. Furthermore, they will be able to communicate quantitative results rigorously and effectively using formal mathematical language. The course fosters autonomous learning skills to further explore advanced quantitative modeling in economics, finance, and insurance. It consolidates a methodological foundation essential for advanced studies in Quantitative Finance, Financial Methods and Models, Time Series Analysis, and more generally for preparing students for advanced academic pathways, such as specialized master’s programs and PhD research in quantitative fields.

Educational objectives

The course introduces students to the mechanisms governing the operation of capital markets at the international level and to the international regulation of financial and intermediary operations. It presents the main quantitative tools for macro-financial analysis and models to interpret real economic and financial phenomena, with the aim of providing recommendations to public and private stakeholders. By the end of the course, students will be able to interpret the evolution of markets and understand the relevant European and international banking and capital market regulations. They will have practical skills to conduct analyses of globally systemic banks, gather documentation, and formulate assessments. Students will be able to critically examine information, even if incomplete, and apply the most appropriate analytical tools, including specialized software for simulations on banking and financial markets. They will acquire mastery of international financial terminology, enabling effective communication with industry professionals, and will be able to present and critically discuss strategic issues in financial contexts. The course also fosters autonomous learning of financial market regulations and practices, allowing continuous updating on emerging instruments, regulations, and trends in banking and capital markets.

Educational objectives

The course introduces the fundamentals of data analysis and statistical inference methodologies for the quantitative analysis of phenomena, with particular attention to economic and financial applications. It covers the main statistical models, regression techniques, classification, clustering, and dimensionality reduction methods. These models and techniques are applied to real-world case studies using specialized statistical software, which also allows students to deepen their understanding of theoretical models and their practical applicability. By the end of the course, students will be familiar with the main statistical methods and models used in economic and financial analysis. They will have developed sensitivity to empirical data analysis, and will be able to select the most appropriate statistical procedure for a given context. Students will be able to analyze data, study variability, and identify relationships between two or more variables (qualitative and/or quantitative). Given a real-world problem, they will be able to define the statistically optimal strategy to address it, apply inference methods using specialized software, interpret the results accurately, and communicate and discuss outcomes using appropriate formal language, including the preparation of structured reports. The course also fosters autonomous study skills and equips students to explore advanced statistical methodologies independently.

Educational objectives

The course provides students with the knowledge necessary to analyze and evaluate the adoption of Artificial Intelligence (AI) and Machine Learning (ML) techniques for developing new financial business models and trading strategies. It is designed for students interested in the applications of AI in the banking and financial markets and aims to provide both a theoretical foundation of AI-based procedures and practical examples of how these cutting-edge techniques are applied, analyzing their effects and implications on business operations. By the end of the course, students will have a solid understanding of the origins of AI, with a focus on widely used Machine Learning technologies, as well as the technological factors supporting business and their practical applications in banking and financial markets. Students will acquire the skills necessary to solve real-world problems: they will be able to identify the problem, determine the most appropriate AI approach, apply the methodologies learned, develop a solution, and evaluate its validity and relevance in the study context.

Educational objectives

The course presents the fundamental principles of banking and financial market regulation and discusses the main transformations of the system following the 2007 financial crisis, with particular attention to the European and national regulatory framework. It illustrates the functioning of supervisory and risk management mechanisms, also through the presentation and analysis of real case studies. By the end of the course, students will be able to apply in practice the principles and rules of banking and financial regulation. They will be capable of analyzing real cases and assessing the operational implications of regulations and the impact of regulatory decisions on financial system stability and intermediaries’ activities. Students will develop the ability to formulate autonomous evaluations of regulatory choices, discussing the effectiveness and limitations of regulatory and institutional tools and providing judgments based on empirical evidence and theoretical references. They will be able to communicate clearly and rigorously on banking and financial regulatory issues, using appropriate technical and legal-economic language. Furthermore, students will acquire the ability to autonomously update their knowledge in an evolving regulatory environment, analyze new directives, and develop a method of study enabling them to pursue advanced studies and professional activities in banking, finance, and regulation.

Educational objectives

The course presents mathematical models that govern the term structure of interest rates and illustrates pricing techniques for financial instruments whose underlying assets evolve according to discrete- and continuous-time models. Topics such as credit risk and the valuation of interest rate derivatives are also addressed. By the end of the course, students will have acquired the theoretical foundations of market and derivative finance, will be able to identify the characteristics and functions of key financial instruments, and understand the mechanisms governing their pricing. They will be able to analyze financial phenomena using advanced quantitative modeling, evaluating model assumptions and limitations to adapt them to specific pricing problems. Students will develop independent judgment, make methodological choices while discussing their effectiveness and implications, and formulate autonomous evaluations of major financial phenomena. They will be able to communicate their analyses clearly and accurately, using technical language appropriate to the audience. Finally, students will be capable of autonomously updating and deepening their quantitative and methodological knowledge in finance, preparing them both for advanced study and professional roles in the financial sector.

Educational objectives

The course introduces students to the main methodologies of constrained, continuous, and discrete optimization. It covers theoretical models for formulating decision problems as optimization problems, with particular emphasis on algebraic models of mathematical programming. The course also presents applications of optimization tools for solving decision-making problems, especially in portfolio selection, including practical laboratory sessions where students solve real economic and financial problems using specialized optimization software. By the end of the course, students will understand the major classes of continuous and discrete optimization models, particularly those most relevant for economic and financial applications. They will be able to identify decision problems suitable for an optimization approach, formulate appropriate model assumptions, and apply optimization software to implement models and obtain solutions. Students will interpret results correctly, critically assess their validity, and discuss their significance in real-world contexts. They will be able to present models and results rigorously using formal technical language. The combination of theoretical learning and practical application will develop students’ autonomy in problem analysis, systematic study methods, and the ability to independently learn new or advanced topics. Upon completion, students will possess a solid quantitative knowledge base and a formal approach to problem analysis, enabling autonomous learning for further studies or professional applications.

Educational objectives

The course introduces the main techniques for analyzing time series, particularly in the economic and financial domains. It presents the theoretical foundations of the subject and the quantitative models most commonly applied to the study of phenomena that evolve over time. The methodologies for building models are illustrated, including empirical analyses of case studies using real data. By the end of the course, students will be familiar with the principal statistical and econometric models for the study of time series and will know how to apply them in practice. They will develop sensitivity to empirical data analysis and autonomy in the use of specialized statistical software. Students will be able to critically evaluate the adequacy of different models and their underlying assumptions across a wide range of applications based on time series, particularly in financial contexts where the study of series volatility plays a central role in relation to associated risk aspects. They will be capable of analyzing the performance of quantitative analyses and will know how to interpret and critically discuss the solutions provided by formal models. They will also develop communication skills to draft structured reports and effectively present the results of their analyses. Finally, they will acquire the ability for autonomous learning to deepen their knowledge of new models and methodologies, which are essential for continuing their studies or for professional training in the quantitative field.

Educational objectives

The educational regulations 270 provide, within each Degree Program, a specific number of credits to be allocated to "student's elective activities." The number of credits provided for this course is 9. These activities consist of exams related to modules offered in the Master's Degree programs of the Faculty or other Faculties at Sapienza.

Educational objectives

After the courses the students will have knowledge and will be able to apply the main models and computational techniques to deal with financial and actuarial problems.
Furthermore the students will be able to discuss the chosen models and will be able to test their skills of analysis as well as communication.
Students will have the basics that are indispensable to continue the studies such as PhD or master in finantial or actuarial fields, and to acquire the skills to pass the tests certification to practice as profession of Actuary.