Finance and insurance

Educational objectives

The course provides students with the essential foundations of linear algebra, multivariable functions, unconstrained and constrained optimization, and solution methods for differential equations. These topics constitute the mathematical background necessary for implementing mathematical models in economics and finance. Students who successfully pass the exam will be able to understand and apply economic and financial modelling techniques. They will be able to use fundamental mathematical tools for analyzing financial problems (such as matrix diagonalization, examination of properties of multivariable functions, maximization/minimization of functions with or without constraints, and solving differential equations and systems) consistently with economic and financial theories. They will acquire knowledge of mathematical models and the ability to apply these methodologies to real problems, identifying the most appropriate model and correctly interpreting the results. The teaching approach, based on theoretical lectures and guided exercises, supports the development of independent judgment in the selection of mathematical tools, communication skills in presenting quantitative results, and autonomous learning abilities in pursuing advanced topics. Therefore, the course represents a fundamental pillar of the study program, closely related to the course Probability and Stochastic Processes for Insurance and Finance, and essential for subsequent courses such as Risk Theory, Quantitative Finance, Methods and Models for Finance, Time Series Analysis, and Actuarial Mathematics for Private Insurance.

Educational objectives

The course provides students with a solid and coherent understanding of the functioning of international economic and financial systems, analysing their structural characteristics, evolutionary dynamics, and the main factors influencing their changes. Both theoretical and empirical economic models are presented, aimed at understanding and assessing the phenomena that characterize modern financial markets. At the end of the course, students will be able to understand and apply the main models of financial economics for asset valuation and market analysis. They will be able to use quantitative and methodological tools to process data, critically interpret results, and compare different analytical approaches.
Students will also acquire a technical vocabulary appropriate to the economic–financial context and the ability to integrate theoretical and applied knowledge within a coherent conceptual framework. The course design, which combines theoretical exposition and applied exercises, promotes independent judgment in the analysis of economic and financial phenomena, communication skills in presenting results, and autonomous learning abilities in exploring new models and analytical tools. Therefore, the course represents a fundamental component of the study program, providing the competences necessary to successfully approach the quantitative and financial courses offered in the second year.

Educational objectives

The course aims to provide students with the fundamental elements of modern probability theory and stochastic processes, with particular reference to models used in quantitative finance and actuarial science. The objective is to offer a rigorous treatment, equipping students with the necessary tools to identify and use the most appropriate models for representing complex real-world phenomena. Students who successfully pass the exam will be able to understand and apply probabilistic tools suitable for modelling uncertainty and for analysing financial and insurance phenomena that evolve over time. They will be able to explain, relate, and compare the main concepts and results, as well as solve problems by combining theoretical knowledge and operational skills.
Since many problems admit alternative solutions, students will develop the ability to critically evaluate different methodologies and select the most appropriate approach to describe a given real (financial or insurance) problem, recognizing its assumptions and limits of applicability. The course also promotes the development of independent judgment in model analysis and result interpretation, communication skills in the use of mathematical and probabilistic language, and continuous learning abilities, thanks to the integration of theoretical lectures, exercises, and individual study. Consequently, students will acquire the fundamental competences required to successfully continue their studies in the quantitative field and to effectively tackle advanced courses such as Quantitative Finance, Methods and Models for Finance, Risk Theory, and Time Series Analysis.

Educational objectives

The course provides the theoretical and practical knowledge necessary for the analysis of economic and financial time series, aiming to develop the ability to interpret data and apply appropriate statistical models to represent the observed phenomena. Students will become familiar with the main modelling and forecasting methods used to analyze the temporal evolution of financial markets and quantify the uncertainty associated with their volatility. Particular attention is given to applied aspects, including the use of statistical software for data processing and model estimation. At the end of the course, students will be able to understand, apply, and critically evaluate the main models for time series analysis, identify the most suitable statistical methodologies for the phenomena under study, and interpret the results independently and rigorously. They will demonstrate independent judgment in selecting models and assessing their performance, as well as communication skills in presenting and discussing results using clear and discipline-appropriate technical language. Students will also develop autonomous and continuous learning abilities, useful for deepening advanced statistical methodologies and pursuing specialization or research paths in quantitative fields.

Educational objectives

The course provides students with an in-depth understanding of economic and financial systems, with particular attention to their structures, operating mechanisms, and the factors driving their evolution across different national and international contexts. The aim of the course is to develop a comparative perspective on major financial systems, fostering an understanding of their role in economic development and in shaping the regulatory dynamics of markets and intermediaries. At the end of the course, students will be able to recognize, understand, and apply theoretical and empirical models useful for analysing the features and evolution of international financial systems. They will be able to critically assess the business models of financial intermediaries, interpret and contextualize the transformations of markets and financial instruments in light of both national and supranational regulatory frameworks, and select the most appropriate solutions to enhance system efficiency. The course design, which combines theoretical analysis with case studies and real-world market examples, promotes the development of independent judgment in evaluating economic and financial dynamics, communication skills for clearly and rigorously presenting complex concepts to both specialist and non-specialist audiences, and autonomous learning abilities to update and expand knowledge in response to market and regulatory evolution. The competences acquired will therefore enable students to consolidate the analytical foundations necessary to successfully pursue advanced courses in the economic–financial area and to prepare for future professional engagement.

Educational objectives

The course provides students with the theoretical, methodological, and computational tools necessary for the valuation of derivative securities in major financial markets. The treatment of pricing models and related numerical techniques is accompanied by practical implementation using quantitative analysis software, also employed for calibrating models to market data.
Students who successfully complete the exam will be able to understand the economic and financial logic of derivative contracts and apply the main stochastic valuation models based on the no-arbitrage principle, in both discrete and continuous time. They will be able to analyze and compare different numerical methodologies, identifying the most efficient and coherent solution for each pricing problem, and translate the theoretical formulation of models into appropriate computational implementations. Exercises and discussion of results will foster autonomous judgment in model selection and calibration, as well as critical evaluation of the outcomes in light of theoretical assumptions and market conditions. Students will also acquire communication skills for presenting quantitative analyses and results, both orally and in writing, using a rigorous and discipline-appropriate technical language. Finally, the course aims to enhance autonomous and continuous learning skills, providing a study and work method that enables independent exploration of developments in financial modelling. The competences acquired will provide a solid foundation for pursuing advanced education, such as second-level master’s programs or doctoral research in quantitative finance.

Educational objectives

The course aims to provide students with practical skills in using the main statistical methods and models for the analysis of univariate time series, with particular reference to financial phenomena. Students will acquire proficiency in statistical software to build interpretative and predictive models and will be able to identify and apply the most appropriate models for studying and forecasting financial market data, taking into account their volatility. Hands-on use of tools such as R will foster a deeper understanding of the functioning of theoretical models and encourage their conscious application in real-world contexts.
At the end of the course, students will have developed a strong empirical data analysis sensibility and practical preparation useful for professional insertion.

Educational objectives

The course provides students with a solid foundation in the mathematical tools essential for constructing, understanding, and applying continuous-time models in financial market analysis, with particular reference to derivative valuation. Building on the fundamentals of stochastic calculus, the main quantitative finance models are covered, including the Black–Scholes–Merton model and its extensions to stochastic volatility (such as the Heston model), as well as the Vasicek, Cox–Ingersoll–Ross, and Hull–White models for the term structure of interest rates. Credit risk modelling, both structural and intensity-based, and the valuation of financial instruments exposed to default risk are also introduced.
While maintaining a theoretical-methodological approach, the course consistently integrates mathematical formalization with real-world applications, developing the ability to recognize, analyze, and interpret volatility, risk, and correlation mechanisms in financial markets. By the end of the course, students will be able to understand, apply, and interpret the main continuous-time mathematical finance models, using stochastic calculus techniques for the analysis and valuation of derivatives and interest rate instruments. They will be able to autonomously select the most appropriate modelling approach for different financial contexts, critically evaluating methods and results. The analytical and rigorous approach of the course also fosters autonomous judgment in model selection and evaluation, communication skills for presenting results, and autonomous learning for exploring new developments in quantitative finance. The skills acquired will enable students to successfully pursue advanced education, such as second-level master’s programs or doctoral research, or to enter the professional field in quantitative finance, risk management, and financial market analysis.

Educational objectives

The course provides the theoretical and practical knowledge necessary to understand and apply the main models and methods of corporate valuation, with reference to approaches adopted in professional practice and international financial markets. Particular attention is given to the valuation of industrial, financial, and insurance companies, as well as to extraordinary operations such as mergers, acquisitions, and initial public offerings. Students will acquire mastery of the fundamentals of corporate finance and develop the ability to analyze the economic and financial structure of companies, reclassify financial statements prepared according to national accounting standards or IAS/IFRS, and assess corporate value creation. At the end of the course, students will be able to critically understand and apply the main corporate valuation methodologies, independently analyze complex economic and financial situations, and evaluate managerial and strategic choices underlying valuation processes. They will demonstrate independent judgment in applying different valuation criteria and formulating assessments consistent with the results of their analyses. Students will also develop communication skills appropriate for clearly and rigorously presenting valuation results and preparing well-founded valuation reports. Finally, they will acquire autonomous and analytical learning abilities, essential for addressing corporate issues rigorously from a quantitative perspective and for pursuing, if desired, further specialization in finance or professional practice.

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 course provides students with an in-depth understanding of the national and European regulatory framework governing financial markets, with particular attention to the supervision exercised by competent authorities over markets and authorized entities. The main characteristics of financial products and instruments, market regulation, and intermediary conduct are also analyzed.
At the end of the course, students will be able to understand and interpret the complex regulatory system (EU directives, Italian Consolidated Finance Act, CONSOB regulations, CONSOB decisions) that governs financial markets in their various components: instruments, intermediaries, market organization, issuers, and auditing firms. Analysis and discussion of regulatory texts will allow students to develop mature critical and interpretative skills, useful for understanding the evolution of financial market law. Students will also develop appropriate technical-legal language, necessary for presenting and discussing learned topics clearly and rigorously, both orally and in writing. Finally, the course helps consolidate autonomous learning skills, providing a study and analytical method that enables students to independently explore regulatory developments in the sector and prepare adequately for post-graduate specialization programs.

Educational objectives

The course aims to provide students with practical skills in using the Python programming language to tackle concrete problems in finance, including market data analysis, risk management, and the implementation of computational algorithms. Lectures will cover Python syntax, the main libraries for data manipulation, retrieval and visualization of financial data, as well as scientific computing tools and some elements of machine learning applied to finance.
The laboratory approach, alternating between instructor explanations and practical coding activities, is designed to develop operational autonomy, analytical skills, and critical awareness in the use of computational tools. By the end of the course, students will be able to design and implement computational solutions for financial problems, understand and explain the operation of Python code and the algorithms implemented. They will acquire skills in identifying the most appropriate techniques, using Python libraries, and critically interpreting results. The training provided will enhance the ability to make independent judgments on methodological choices, communicate results clearly both orally and in writing, and consolidate an autonomous learning method useful for further computational and financial studies. The skills acquired complement the theoretical training, preparing students for professional engagement in finance or for pursuing advanced study 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 final thesis of the Master’s degree consists of the preparation and discussion of a dissertation, which 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 in-depth methodological and experimental experience, in which the student integrates knowledge acquired across the program, engages with 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 work also fosters collaborative skills through interactions with faculty and peers and strengthens the ability to communicate analysis results clearly, concisely, and technically, with particular attention to presenting and arguing investment, hedging, and risk management strategies. At the end of the program, students will be able to independently update their quantitative and regulatory skills according to market developments and evolving risk management techniques. The thesis certifies scientific maturity and critical autonomy necessary to pursue advanced studies, such as second-level Master’s programs and PhDs, and provides solid preparation for the actuarial professional exam or professional entry into complex financial and insurance contexts.

Educational objectives

The course provides students with the essential foundations of linear algebra, multivariable functions, unconstrained and constrained optimization, and solution methods for differential equations. These topics constitute the mathematical background necessary for implementing mathematical models in economics and finance. Students who successfully pass the exam will be able to understand and apply economic and financial modelling techniques. They will be able to use fundamental mathematical tools for analyzing financial problems (such as matrix diagonalization, examination of properties of multivariable functions, maximization/minimization of functions with or without constraints, and solving differential equations and systems) consistently with economic and financial theories. They will acquire knowledge of mathematical models and the ability to apply these methodologies to real problems, identifying the most appropriate model and correctly interpreting the results. The teaching approach, based on theoretical lectures and guided exercises, supports the development of independent judgment in the selection of mathematical tools, communication skills in presenting quantitative results, and autonomous learning abilities in pursuing advanced topics. Therefore, the course represents a fundamental pillar of the study program, closely related to the course Probability and Stochastic Processes for Insurance and Finance, and essential for subsequent courses such as Risk Theory, Quantitative Finance, Methods and Models for Finance, Time Series Analysis, and Actuarial Mathematics for Private Insurance.

Educational objectives

The course provides students with a solid and coherent understanding of the functioning of international economic and financial systems, analysing their structural characteristics, evolutionary dynamics, and the main factors influencing their changes. Both theoretical and empirical economic models are presented, aimed at understanding and assessing the phenomena that characterize modern financial markets. At the end of the course, students will be able to understand and apply the main models of financial economics for asset valuation and market analysis. They will be able to use quantitative and methodological tools to process data, critically interpret results, and compare different analytical approaches.
Students will also acquire a technical vocabulary appropriate to the economic–financial context and the ability to integrate theoretical and applied knowledge within a coherent conceptual framework. The course design, which combines theoretical exposition and applied exercises, promotes independent judgment in the analysis of economic and financial phenomena, communication skills in presenting results, and autonomous learning abilities in exploring new models and analytical tools. Therefore, the course represents a fundamental component of the study program, providing the competences necessary to successfully approach the quantitative and financial courses offered in the second year.

Educational objectives

The course aims to provide students with the fundamental elements of modern probability theory and stochastic processes, with particular reference to models used in quantitative finance and actuarial science. The objective is to offer a rigorous treatment, equipping students with the necessary tools to identify and use the most appropriate models for representing complex real-world phenomena. Students who successfully pass the exam will be able to understand and apply probabilistic tools suitable for modelling uncertainty and for analysing financial and insurance phenomena that evolve over time. They will be able to explain, relate, and compare the main concepts and results, as well as solve problems by combining theoretical knowledge and operational skills.
Since many problems admit alternative solutions, students will develop the ability to critically evaluate different methodologies and select the most appropriate approach to describe a given real (financial or insurance) problem, recognizing its assumptions and limits of applicability. The course also promotes the development of independent judgment in model analysis and result interpretation, communication skills in the use of mathematical and probabilistic language, and continuous learning abilities, thanks to the integration of theoretical lectures, exercises, and individual study. Consequently, students will acquire the fundamental competences required to successfully continue their studies in the quantitative field and to effectively tackle advanced courses such as Quantitative Finance, Methods and Models for Finance, Risk Theory, and Time Series Analysis.

Educational objectives

The course introduces students to risk theory in the insurance context, with particular focus on probabilistic techniques and models for managing a non-life insurance company, as well as on risk measures and reinsurance contracts. Students will gain an in-depth understanding of the mathematical and probabilistic tools necessary to analyze key issues in insurance markets, such as assessing the solvency of an insurance company, analyzing various reinsurance contracts, and estimating their impact on the risk measures used by insurers.
By the end of the course, students will be able to analyze and formalize practical problems in insurance and reinsurance, selecting the most appropriate mathematical and probabilistic models and applying them effectively, including stochastic aspects when relevant. They will be able to critically evaluate results and draw well-founded conclusions, developing independent judgment in identifying the most suitable modeling approach and selecting the most efficient methodologies for each problem. Students will also develop communication skills to present analyses and arguments clearly and rigorously, both orally and in writing, tailoring the language to the type of audience, whether specialist or non-specialist. Simultaneously, they will acquire the ability to organize and independently update their learning, consolidating a study method that enables them to acquire new knowledge and skills, both in professional contexts and in advanced academic pathways, such as second-level master programs or doctoral studies.

Educational objectives

The course provides students with an in-depth understanding of economic and financial systems, with particular attention to their structures, operating mechanisms, and the factors driving their evolution across different national and international contexts. The aim of the course is to develop a comparative perspective on major financial systems, fostering an understanding of their role in economic development and in shaping the regulatory dynamics of markets and intermediaries. At the end of the course, students will be able to recognize, understand, and apply theoretical and empirical models useful for analysing the features and evolution of international financial systems. They will be able to critically assess the business models of financial intermediaries, interpret and contextualize the transformations of markets and financial instruments in light of both national and supranational regulatory frameworks, and select the most appropriate solutions to enhance system efficiency. The course design, which combines theoretical analysis with case studies and real-world market examples, promotes the development of independent judgment in evaluating economic and financial dynamics, communication skills for clearly and rigorously presenting complex concepts to both specialist and non-specialist audiences, and autonomous learning abilities to update and expand knowledge in response to market and regulatory evolution. The competences acquired will therefore enable students to consolidate the analytical foundations necessary to successfully pursue advanced courses in the economic–financial area and to prepare for future professional engagement.

Educational objectives

The course aims to provide students with a solid understanding of the main methods and models of actuarial mathematics and their applications in insurance, with particular focus on life and non-life contracts. Students will acquire the knowledge necessary to calculate premiums and reserves for traditional insurance contracts, understand the strategic variables underlying coverage and portfolio diversification, and apply probabilistic and statistical techniques for risk measurement. The course integrates theoretical treatment with practical examples, potentially supported by computational tools, enabling students to develop operational skills in analyzing insurance contracts, evaluating risk measures, and designing products with flexible benefits or alternative coverage. Students will learn to critically interpret actuarial models, select the most appropriate methodologies for specific insurance problems, and clearly and rigorously present results, both orally and in writing. By the end of the course, students will have developed independent judgment in risk analysis and management, the ability to apply actuarial models critically to real scenarios, communication skills appropriate to the professional context, and autonomous learning methods useful for continuous deepening of advanced actuarial mathematics topics and for subsequent courses such as Risk Theory, Actuarial Theory and Techniques for Pension, and Insurance Techniques and Finance.

Educational objectives

The course provides students with advanced training on new-generation life insurance products and the quantitative tools used for their valuation and management, in accordance with Solvency II regulations and international accounting standards. By the end of the course, students will be able to understand the technical features of revaluable, index-linked, and unit-linked insurance contracts, identify the main sources of risk, and assess their impact on regulatory capital requirements. They will be able to apply quantitative models to determine premiums, mathematical reserves, and solvency requirements, developing operational skills in parameter calibration and model implementation. The course also aims to cultivate actuarial and financial sensitivity in evaluating innovative insurance products, with attention to accounting and prudential aspects under both civil law and IAS/IFRS frameworks. Particular emphasis is placed on acquiring specialist technical language, effectively communicating analysis results, and developing the ability for independent updating on quantitative models and regulatory developments in the insurance sector.

Educational objectives

The course provides students with an in-depth understanding of actuarial and quantitative models for the evaluation of pension benefits and public and private pension systems. The teaching covers the technical, financial, and demographic foundations underlying pay-as-you-go and funded schemes, as well as the national and European regulatory framework for mandatory and supplementary pensions. By the end of the course, students will be able to apply actuarial models to calculate contributions and benefits, assess the financial sustainability of pension systems even in complex scenarios, and estimate technical-financial balance indicators. They will be able to interpret demographic, economic, and regulatory data to provide independent and well-reasoned assessments of pension policies, and communicate analysis results clearly through reports and professional opinions according to industry standards. The course also develops autonomous study skills and the ability for continuous updating, integrating actuarial knowledge with quantitative and digital tools for simulating and evaluating complex pension scenarios. This provides a solid foundation for professional actuarial practice, broader professional applications, and access to postgraduate specialization programs.

Educational objectives

The course aims to provide students with a solid understanding of insurance company law and insurance contracts, combining the analysis of codified legal norms with regulatory provisions. Students will acquire tools to critically interpret legal rules and understand their operational applications, developing the ability to classify facts and select the relevant regulatory framework. By the end of the course, students will be able to analyze legal texts and insurance contracts, critically assessing their content and operational implications, even in moderately complex contexts. They will also be able to independently formulate reasoned judgments on judicial rulings and supervisory authority acts, demonstrating analytical autonomy and legal reasoning skills. The course promotes the development of communication skills, enabling students to present and discuss legal topics using appropriate technical language, both orally and in writing, and to interact effectively with different audiences. Finally, students will acquire methods and tools to independently deepen their knowledge of new legal developments, fostering a critical and systematic learning approach useful for both professional practice and advanced post-graduate studies.

Educational objectives

The course provides the theoretical and practical knowledge necessary to understand and apply the main models and methods of corporate valuation, with reference to approaches adopted in professional practice and international financial markets. Particular attention is given to the valuation of industrial, financial, and insurance companies, as well as to extraordinary operations such as mergers, acquisitions, and initial public offerings. Students will acquire mastery of the fundamentals of corporate finance and develop the ability to analyze the economic and financial structure of companies, reclassify financial statements prepared according to national accounting standards or IAS/IFRS, and assess corporate value creation. At the end of the course, students will be able to critically understand and apply the main corporate valuation methodologies, independently analyze complex economic and financial situations, and evaluate managerial and strategic choices underlying valuation processes. They will demonstrate independent judgment in applying different valuation criteria and formulating assessments consistent with the results of their analyses. Students will also develop communication skills appropriate for clearly and rigorously presenting valuation results and preparing well-founded valuation reports. Finally, they will acquire autonomous and analytical learning abilities, essential for addressing corporate issues rigorously from a quantitative perspective and for pursuing, if desired, further specialization in finance or professional practice.

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 provides students with computational tools based on the Python programming language to tackle practical problems in actuarial and insurance contexts. During the laboratory sessions, students will explore Python syntax and the main libraries for retrieving, manipulating, and visualizing actuarial data, as well as scientific computing libraries and machine learning tools applied to actuarial problems. The teaching approach is practice-oriented: instructor explanations alternate with direct coding implementation by the students, who apply the knowledge acquired to solve real problems. In this way, students develop autonomy in selecting the most appropriate computational techniques, communication skills for presenting results, and the ability to independently learn new tools and methodologies. By the end of the course, students will be able to approach actuarial problems with a quantitative Python-based approach, implement algorithms, interpret results, and present effective solutions. The skills acquired complement the theoretical training provided by other courses, facilitating professional entry into actuarial or risk management roles and enabling access to advanced training programs.

Educational objectives

The final thesis of the Master’s degree consists of the preparation and discussion of a dissertation, which 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 in-depth methodological and experimental experience, in which the student integrates knowledge acquired across the program, engages with 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 work also fosters collaborative skills through interactions with faculty and peers and strengthens the ability to communicate analysis results clearly, concisely, and technically, with particular attention to presenting and arguing investment, hedging, and risk management strategies. At the end of the program, students will be able to independently update their quantitative and regulatory skills according to market developments and evolving risk management techniques. The thesis certifies scientific maturity and critical autonomy necessary to pursue advanced studies, such as second-level Master’s programs and PhDs, and provides solid preparation for the actuarial professional exam or professional entry into complex financial and insurance contexts.

Educational objectives

The course provides students with the theoretical and practical foundations of probability theory and stochastic processes, which are essential tools for analyzing and modeling economic and financial phenomena. Students will learn how to formalize uncertainty, describe and interpret random phenomena using probabilistic models, and apply such models to analyze data variability, particularly the variability associated with financial market risk. By the end of the course, students will be familiar with the main stochastic models used in finance and insurance, will be able to solve quantitative problems through analytical methods, and will know how to select and apply the most appropriate model for a given economic or financial context. They will apply probabilistic models and techniques to describe and study random phenomena, assessing the efficiency of quantitative tools used in financial asset management and insurance contracts. Students will be able to analyze random phenomena over time, choose appropriate models, and interpret results critically, assessing their validity and reliability. They will be able to communicate quantitative results rigorously and effectively, using formal language correctly. Moreover, they will develop autonomous learning skills to deepen their understanding of advanced quantitative modeling. Finally, they will consolidate a methodological foundation useful for pursuing further studies in quantitative applications to finance and essential for successfully following advanced courses such as Quantitative Finance, Methods and Models for Finance, and Time Series Analysis.

Educational objectives

The course illustrates the mechanisms governing the functioning of capital markets at the international level and presents the methodologies adopted by commercial banks, investment banks, and international regulatory bodies in financial and intermediation operations. It also provides both European and international regulatory knowledge concerning banking systems and capital markets. By the end of the course, students will understand the mechanisms that regulate the operation of international banking and capital markets. They will be able to interpret the evolution of global financial markets and will be familiar with the main quantitative models used for macro-financial analysis. They will acquire the practical skills required to analyze a globally systemically important bank, collecting the necessary documentation and applying the tools learned in the course to assess its performance, identify deviations from best practices, and detect areas of risk. Students will be able to carry out evaluations by integrating economic, regulatory, and quantitative knowledge to analyze the stability and efficiency of banking and capital markets. They will critically assess even incomplete information and select the most appropriate analytical tools. They will master the international financial and technical terminology necessary to communicate effectively with sector professionals, and they will develop the ability to present and critically discuss strategic issues in global financial contexts.
Finally, students will develop a critical and autonomous learning approach to the rules and practices of international financial markets, as well as the ability to stay up to date on new instruments, regulations, and emerging trends in the banking and capital markets sectors.

Educational objectives

The course provides students with advanced mathematical knowledge essential for the quantitative analysis of economic and financial phenomena and for the construction of interpretative and predictive models. Students will study the theory of linear transformations and the analysis of eigenvalues and eigenvectors, which are fundamental for representing and summarizing complex economic and financial data; the study of multivariable functions and optimization techniques, used to analyze problems of resource allocation and portfolio management; and solution methods for ordinary differential equations, applied to the dynamic modeling of interest rates, asset prices, and other macroeconomic variables. By the end of the course, students will have acquired solid knowledge of economic and financial modeling and will be able to rigorously apply fundamental mathematical tools to solve economic and financial problems. They will be capable of assessing real-world issues, identifying and selecting appropriate mathematical models and methodologies, and correctly interpreting results within the economic and financial context under study. They will be able to present the results of quantitative analyses clearly and rigorously, illustrating the methodologies and models employed using formal language. Students will have developed a critical and autonomous study method, essential for successfully completing the advanced courses in the Finass master’s degree program, such as Risk Theory, Quantitative Finance, Methods and Models for Finance, Time Series Analysis, and Actuarial Mathematics for Private Insurance.

Educational objectives

The course introduces students to the foundations of statistical inference and the main methodologies of data science, with a specific focus on economic and financial applications. It presents the principal statistical models and techniques for regression, classification, clustering, and dimensionality reduction. By the end of the course, students will be familiar with the main statistical models and methods used for analysis in the economic, financial, and insurance domains. They will be able to identify the most appropriate methodologies for each problem and use statistical software for computation and data analysis to implement them. Students will apply statistical inference methods to real data for empirical analysis, correctly interpret model results, and assess their validity within the study context. They will develop autonomy in selecting the most suitable models for different analyses, justifying their choices based on complexity, interpretability, and predictive performance. They will be able to communicate results effectively through clear and coherent reports, integrating both code and analytical outputs. Finally, they will acquire an autonomous study method and the tools to deepen their understanding of new, including advanced, statistical methodologies, with the ability to implement them in a programming language.

Educational objectives

The course covers the theoretical foundations of Artificial Intelligence (AI) applied to finance, with a focus on Machine Learning techniques and neural networks. Its aim is to illustrate the use of AI in banking and financial business models, as well as to analyze the impact of adopting these technologies in economic and financial systems, including at the international level. The course provides both theoretical knowledge and practical methodologies that allow students to leverage state-of-the-art AI techniques for addressing problems in banking and finance. By the end of the course, students will have acquired the knowledge to analyze and evaluate the adoption of AI technologies in the banking and financial sector, particularly in the use of Machine Learning for developing new financial business models and trading strategies. Students will be able to identify the most suitable modeling approach for a given financial, insurance, or pension context; critically evaluate the adequacy of AI approaches according to the specific problem and select the most appropriate technique; use software and applications to conduct empirical analyses and implement the quantitative models learned; assess the appropriateness of AI techniques in context, considering ethical and regulatory implications; present results clearly and effectively through visualizations and technical reports, using professional and internationally appropriate technical language; continuously update their skills and adapt learned techniques to new banking and financial problems.

Educational objectives

The course provides students with a solid and in-depth understanding of the theoretical principles and quantitative tools necessary to comprehend the functioning of financial markets and the pricing of derivative instruments. Particular attention is given to valuation models and the arbitrage mechanisms that ensure their consistency, integrating theoretical analysis with practical examples and quantitative calculation tools. By the end of the course, students will have acquired the theoretical foundations of market and derivative finance, be able to identify the characteristics and functions of major financial instruments, and understand the mechanisms that determine their prices. They will be able to apply mathematical and statistical models to represent market processes, estimate parameters, value derivatives, and analyze risk, critically interpreting the results obtained and the assumptions underlying the models. Students will develop independent judgment in applying models rigorously and consciously, making methodological choices while assessing their effectiveness, limitations, and economic implications. They will be able to form autonomous evaluations of key financial phenomena and communicate their analyses clearly and precisely, adapting the language to both specialist and non-specialist audiences. Furthermore, they will be able to autonomously update and deepen their quantitative and methodological knowledge in finance. The skills acquired in understanding financial phenomena and using practical problem-solving tools are essential for pursuing advanced studies or entering professional roles in the financial sector.

Educational objectives

The course provides students with fundamental knowledge of banking and financial regulation and the main transformations in the system following the 2007 crisis, with particular attention to European and national regulatory frameworks. It illustrates the objectives, logic, and instruments of prudential regulation, as well as the functioning of supervisory mechanisms and risk management processes. By the end of the course, students will be able to apply in practice the principles and rules of banking and financial market regulation, analyze real cases and evaluate the operational implications of regulatory norms, understand the impact of regulatory decisions on financial system stability and the activities of intermediaries, and form independent evaluations of regulatory choices, discussing the effectiveness and limitations of legal and institutional tools. They will be able to interpret regulatory phenomena and express informed judgments based on evidence and theoretical references. Students will also be able to communicate clearly and rigorously on banking and financial regulation topics, using appropriate technical and legal-economic language, update their knowledge autonomously in a constantly evolving regulatory environment, analyze new directives, and acquire the knowledge and methods necessary for advanced studies and professional activities in banking, finance, and regulatory sectors.

Educational objectives

The course introduces students to the main methodologies of constrained, continuous, and discrete optimization. It presents the tools necessary to formally represent decision problems through optimization models, with particular attention to mathematical programming, both linear and nonlinear, as well as graph-based models and network optimization techniques. Students acquire a set of specialized methodologies for the quantitative study of financial problems, particularly in portfolio optimization. The theoretical lessons cover the main classes of optimization models and the correct methodology to formalize them. Practical lessons focus on applying these models to real-world economic and financial problems, with numerous examples and systematic implementation exercises using dedicated optimization software.
By the end of the course, students will be familiar with the most important classes of continuous and discrete optimization models, especially those relevant for economic and financial applications. They will be able to identify decision problems that require an optimization approach, select the correct assumptions to formulate the most appropriate model, and competently use optimization software to implement models and find solutions. Students will be able to interpret results accurately, discuss their validity, and understand their meaning in real-world contexts, using the insights gained to potentially improve the model itself. They will be able to present models and results rigorously, employing formal technical language appropriately. The combination of theoretical analysis and practical use of optimization tools develops students’ autonomy in problem solving, providing a systematic method of study and the ability to learn autonomously new topics, including those that are new or more advanced with respect to the course program.

Educational objectives

The course introduces the main techniques for analyzing economic and financial time series, integrating graphical and analytical approaches with particular attention to risk aspects. It presents the theoretical foundations of time series analysis and the most widely used models for studying phenomena that evolve over time, illustrating methods for constructing statistical and econometric models, also through empirical data analysis. By the end of the course, students will be familiar with the models most commonly used to study time-evolving financial phenomena. They will be able to recognize the characteristics of financial data and make informed choices about which statistical model to apply for forecasting and quantifying risk and uncertainty. Students will develop sensitivity to empirical data analysis and autonomy in using statistical software for time series analysis. They will be able to explore, describe, and model real-world time series, estimate parameters, conduct diagnostic analyses, and generate reliable forecasts while critically justifying their choices. They will be able to evaluate the adequacy of different models and methods for a wide range of applications on time series, particularly in financial contexts where volatility is central. Students will develop the ability to make decisions regarding model selection and the assessment of underlying assumptions, analyze model performance, and interpret and discuss results critically. They will acquire communication skills for preparing clear, structured reports and effectively presenting results, integrating code, outputs, and interpretations. Finally, students will develop autonomous learning skills to explore new models and methodologies, essential for pursuing advanced studies in quantitative finance.

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 final thesis of the Master’s degree consists of the preparation and discussion of a dissertation, which 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 in-depth methodological and experimental experience, in which the student integrates knowledge acquired across the program, engages with 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 work also fosters collaborative skills through interactions with faculty and peers and strengthens the ability to communicate analysis results clearly, concisely, and technically, with particular attention to presenting and arguing investment, hedging, and risk management strategies. At the end of the program, students will be able to independently update their quantitative and regulatory skills according to market developments and evolving risk management techniques. The thesis certifies scientific maturity and critical autonomy necessary to pursue advanced studies, such as second-level Master’s programs and PhDs, and provides solid preparation for the actuarial professional exam or professional entry into complex financial and insurance contexts.