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

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

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 goal of this course is to describe the main pricing methodologies for financial instruments, when the underlyings are governed by either discrete-time and continuous-time stochastic processes, with particular emphasis on the Black-Scholes-Merton model. Moreover, the course provides computational tools for pricing and hedging. The main topics will be introduced from a theoretical perspective. Furthermore, they will be analyzed from a computational point of view, using MATLAB software.

• (Knowledge and understanding) At the end of the course, students will be able to apply the main numerical methodologies for financial derivatives pricing, both in discrete-time and continuous-time diffusion market models. They will also be able to understand and illustrate the main characteristics of each numerical method and to recognize the most effective solution to the economic-financial problem they will face. Finally, they will manage to apply the theoretical framework to practical experiences, in order to obtain the fair value of derivative securities.

• (Applying knowledge and understanding) The students who pass the exam can identify the suitable model to describe the financial structure, and also establish the most efficient methodologies to solve the related financial issues.

• (Making judgements) By using the information inferred from the lectures, students autonomously may inspect the financial context, take into account the whole range of methods to use, and interpret the obtained results.

• (Communication skills) After passing the exam (that consists of a written/practical text with open-ended questions and/or exercises and/or practical works with Matlab), students will be able to adequately outline the main topics covered by the lectures, either verbally or through written documents.

• (Learning skills) Standard lectures, lab activities and self-study allow students to develop a method to autonomously acquire new financial knowledge and theoretical\practical skills.

Educational objectives

This course intends to provide mathematical tools used to define and investigate continuous-time models devoted to the evaluation of the fair value of derivative securities within the main financial markets.

Specific goals:

- At the end of the lectures, students will be able to apply standard stochastic calculus tools to financial problems. Furthermore, they can understand and explain the main models that describe the dynamics of stochastic processes involved in characterizing specific financial variables, such as interest rate term structure and equity derivatives. Students will also learn how to apply theoretical rules to practical experiences.

- Students who pass the exam can identify the suitable model to describe the financial structure, and also establish the most efficient methodologies to solve the related financial issues.

- By using the information inferred from the lectures, students may autonomously inspect the financial context, take into account the whole range of methods to use, and interpret the obtained results.

- After passing the exam (that consists of a written text with open-ended questions and/or exercises), students will be able to adequately outline the main topics covered by the lectures, either verbally or through written documents.

- Standard lectures and self study allow students to develop a method to autonomously acquire new financial knowledge and theoretical\practical skills.

Educational objectives

General goals:
In this course students will learn to formulate models to tackle relevant finance and insurance problems using several mathematical and statistical tools mostly related to optimization theory.
They will also learn to use, understand, and develop computational tools suitable for the solution of the models proposed.

Specific goals:
- At the end of the course, students will have a sound knowledge of portfolio selection theory and of the main algorithms used to solve optimization problems. They will also know the main optimization models used in finance and insurance applications.
- This course will enable students to address several practical problems in finance and insurance with the aid of quantitative models and with the use of computational tools for their solution
- After seeing a careful analysis of the critical issues related to the models presented in the course, the students will be aware of the relations between models and real problems to which they are applied and will be able to identify the essential elements that should be used in a model.
- The students have to deliver a written report on a project and to orally describe some of the topics presented in the course to pass the exam. They will therefore acquire the capability to communicate their knowledge in a suitable way.
- Having conducted autonomous researches for the projects required for the course, with possible support from the teacher when necessary, students will be subsequently capable to deepen and continue the studies in this field.

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.

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

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

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 aims to introduce the main methods and models of Actuarial Mathematics and to illustrate their application in the insurance field. The course focuses more precisely on the assessment of life and non-life insurance contracts and explores the theoretical principles, application problems and computational aspects.
The course provides in particular the formulas and tools for calculating the premiums and reserves of traditional life insurance contracts and illustrates the strategic variables underlying the hedging, diversification and formation of portfolio profit. It also illustrates the charging methods and techniques of non-life insurance, focusing on the mathematical-probabilistic bases for calculating the total claims amount even in the non-insurance sector. Finally, the course provides the theoretical principles necessary for the evaluation of the financial options incorporated in insurance products with flexible services and for the choice among forms of cover alternative to insurance and reinsurance.
The course requires a good knowledge of Mathematical Analysis, Financial Mathematics and Probability acquired in three-year degree courses and of Mathematics for the economics and companies - Advanced course and of Probability and Stochastic Processes. Futhermore it is closely related to the courses Risk Theory, of the Master's degree course Finass and provides the basis for the subsequent teachings of Actuarial Technique for Previdence and of Tecnique and Finance for Insurance of the same course graduation.

A. Knowledge and understanding

Students who pass the exam, will know the theoretical concepts and principles of Actuarial Mathematics and its applications in the insurance field. They will know the definition of a stochastic financial operation, the concept of actuarial value, the principle of equity and the criterion of expected utility. They will know the main types of life insurance policies and will have acquired the mathematical and computational tools for the calculation of premiums and reserves, both pure and commercial. They will know the probabilistic approach for calculating the total claims amount, the statistical pricing method in non-life insurance and the forms of personalization of the premium. They will know the main operational strategies achievable with the financial options and will be able to derive the methods for constructing and evaluating structured policies and forms of risks coverage different from reinsurance.

B. Applying knowledge and understanding

Students who pass the exam will be able to: calculate the prize and the mathematical reserves of the main life insurance contracts and discuss the results according to the variation of the technical assessment bases; calculate the total claims amount starting from different assumptions regarding the distribution of the number of claims and the individual claim amount; structure and evaluate contracts with flexible services; carry out numerical exemplifications on Excel sheets even using customized functions realized in VBA.

C. Making judgments

Students will develop the ability to set up and solve simple problems of coverage and diversification of insurance policies portfolios by identifying the main strategic variables; will be able to discuss the applicability of the models studied under more general hypotheses and in the presence of multiple sources of uncertainty and will be able to extend them to health insurance and insurance against catastrophe risks; they will be able to study and find the mathematical tools useful for dealing with the quantitative problems raised in practice by the new regulations; will have developed the ability to formalize in actuarial terms problems of measurement and management of non-insurance risks, too.

D. Communication skills

Students will have the opportunity to take the exam by presenting in the classroom a paper written with a colleague of the course and under the supervision of the teacher on a topic of the program: during the study phase, they will be able to test their skills of analysis as well as communication and collaboration with the course colleague and interaction with the teacher. During the writing of the written paper, they will have the opportunity to learn how to write a scientific text and to exercise the descriptive, logical-deductive and exemplifying skills; with the oral presentation, they will have the opportunity to compare themselves with the other course colleagues and to stimulate and involve them with their own arguments.

E. Learning skills

Students will have the basics of Actuarial Mathematics that are indispensable to support the other quantitative area exams required by the master's degree program, but also the tools useful for formalizing, understanding, explaining and solving the problems of risk measurement and management in general.

Educational objectives

The course provides and introduction to the insurance risk theory, and in particular to the probabilistic techniques and models relevant to the non-life insurance business, to the risk measurements, and to reinsurance contracts.
At the end of the course students should be able to
· know and apply the mathematical and probabilistic tools to assess the solvency of an insurance company;
· know the main types of reinsurance and what their effects are on various measures of safety and profitability of the insurance business.

Students who pass the exam will be able to
• evaluate the probability of ruin in a Cramer-Lundberg capital process for examples of similar difficulty as seen in the course
• discuss the key idea in the proof of Lundberg’s inequality and apply it to a Cramer-Lundberg capital process,
• explain how reinsurance can be incorporated in the Cramer-Lundberg model and determine the optimal level of reinsurance for examples of similar difficulty as seen in the course.

Thanks to the activity during the course, students will be able to implement and study models to asses the solvency position of a non-life insurance company

Students having passed the exam shall be able to properly present the topics acquired during the course either orally or in written form

Students having passed the exam will acquire learning skills that allow them to be autonomous in updating and developing their knowledge and competences related to the main risks to which non-life insurance companies are exposed.

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 provide students with an operational introduction to the implementation, through numerical methods, of the theoretical models presented in the Risk Theory course. The course is designed to develop practical and computational skills for the evaluation of insurance and reinsurance contracts and for quantifying the risk associated with potential losses. Using MATLAB software, students learn to translate theoretical probabilistic models into operational tools for insurance risk analysis, with particular focus on the distribution of aggregated claim costs, the evaluation of the probability of ruin, and the use of the main risk measures applied in Risk Management.

Educational objectives

The course aims to provide basic knowledge of Private Insurance law. Subject of study will be insurance company and the insurance contract.

Specific objectives:
- Knowledge of the institutes and disciplines. Ability to understand the themes and problems presented.
- The student will acquire knowledge of law institutions and their rules. Understanding of problems which said rules are established for. Development of critical analysis and not merely receptive learning.
- Students acquire the capacity to correctly interpret the meaning of rules. Ability to qualify facts in order to identify and select the applicable rules.
- Students will develop the ability to clearly and correctly illustrate their knowledge, methods and results of interpretation.
- Students will acquire the ability to evaluate in a systematic framework arguments supporting any thesis. Ability to understand and set in a systematic framework new laws and rules

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 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.

Educational objectives

General goals:

The aim of the course is to provide students with a sound knowledgre of the basic mathematical topics and tools for financial modelling, such as linear algebra, multivariable functions, static optimization methods, and techniques to solve differential equations. Some arguments will focus on the crucial role of the interest rate curve in evaluating financial cash flows.

Specific goals:

Knowledge and comprehension
After attending the course, students will be able to know the evaluation procedures of financial problems and to understand the results of mathematical models used to resolve those problems.

Ability to apply knowledge and comprehension

At the end of the course, students will be able to use basic mathematical tools to evaluate financial problems in accordance with any robust financial theory and to apply a right knowledge in their use to real evaluation problems.

Judgment skills.

At the end of the course students will be able to understand the results derived from the financial tools applied and to explain differences among figures obtained from different models, in relation to the theoretical setting in wich the evaluation is provided.

Communication skills.

After passing the exam, students will be able to explain and discuss about the arguments treated during the course, giving their comments and remarks on the use of the mathematical tools learnt.

Self-learning skills

After passing the exam, students will have a knowledge of the advanced mathematical topics and tools for financial modelling that will permit them to face future studies in mathematical finance for pricing of liquid and illiquid financial instruments.

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 deals with the fundamentals and the main statistical topics of statistical inference, useful for the quantitative analysis of real phenomena, and particularly of financial markets. Students will be also introduced to the statistical software R as a tool for applying statistical methodologies to real data as well as a tool for understanding the statistical theory itself.
Students who pass the exam will know the main concepts and procedures of statistical inference, concerning specific parameters, distributions and regression models.
Students who pass the exam will acquire skills for data analysis: on the base of the methodologies introduced in the course, they will be able to discriminate among different statistical procedure and to choose the most suitable one for the problem under examination. They will be available to study data and to apply data reduction techniques, to investigate the variability of the phenomenon, and to study the relationship with possible explanatory variables (qualitative and/or quantitative) using the statistical software R. Therefore, starting with a real problem, they will be able to determine the best statistical procedure for analyzing the observed data and to obtain results.
They will also be able to analyze in a critical way the obtained results, highlighting pros and cons of the adopted procedures. Students’ critical skill is especially encouraged by the discussion of case studies, which start from a real problem, statistically formalize it, and then show the empirical analysis and critically evaluate the results. The analysis of a case study is also required to students: at the end of the course they will have to produce a report concerning all the phases of the study, including a critical discussion of the results. The evaluation of the report will also concern students’ communication skills and their ability to explain what they learned and the results of the quantitative analysis.
The deep comprehension of the statistical methodologies dealt with in the course, will allow the student to understand also models not described in the course, evaluating in complete autonomy their pros and cons.

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

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.