Actuarial and Financial Sciences

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Curriculum(s) for 2026 - Actuarial and Financial Sciences (33638)

Scienze attuariali

Lesson [SSD] [Language]	Year	Semester	CFU
10627887 \| Statistical methods for finance and insurance [STAT-01/A] [ITA]	1st	1st	9
Educational objectives Learning goals The primary aim of the course is the students' knowledge of the most relevant statistical methods for financial and insurance data. Knowledge and understanding. Knowledge of the most applied statistical techniques in the domains of inference, time series and dependence for for financial and insurance data. Applying knowledge and understanding. Ability to formalize real problems in the fields of finance and insurance in statistical terms and to solve them by applying the corresponding statistical methods. Making judgements. Ability to apply statistical methods and to evaluate the reliability of the results obtained by analyzing real financial and insurance data. Communication skills. By studying and by examples, learning and acquiring technical and scientific language in the statistical domain to be used properly in the final evaluation. Learning skills. Students passing the exams acquire the knowledge for facing issues concerning finance and insurance, in courses devoted to finance and insurance, by means of statistical methods.
10626938 \| Mathematical Models For Financial Markets [STAT-04/A] [ITA]	1st	1st	9
Educational objectives Learning goals The course deals with the topics essential for acting in the financial market. It has the goal of providing the fundamental notions for the formalization and valuation of financial derivatives and for risk management. Knowledge and understanding After attending the course the students are familiar with the principles of valuation of derivative contracts and with some of the main stochastic models for the evaluation of equity, interest rate and credit risk. They are able to appreciate the role of modeling hypotheses in the evaluation process, also from the point of view of numerical complexity. Applying knowledge and understanding After attending the course the students are able to formalize, in a stochastic environment, the problems of pricing and measuring risks of financial contracts. Making judgements Students develop critical skills through the comparison of different financial hypotheses applied to problems of increasing complexity. Communication skills Students, through the study of theory and practical examples, acquire the technical-scientific language of the discipline, which must be used appropriately in the oral examination. Learning skills Students passing the exam have learned a method of analysis that allows them to tackle financial problems involving more complex financial instruments and a broader sets of risks.
10628881 \| Insurance and banking law [GIUR-03/A] [ITA]	1st	1st	6
Educational objectives GENERAL OBJECTIVES The course intends to introduce students to the study of the operational rules of financial markets, with particular regard to insurance. Students must not only learn the basics but also analyse them critically, especially with regard to the sound ratio of their discipline. KNOWLEDGE AND UNDERSTANDING SKILLS After attending the course, the students will know and understand how to deal with the study not only of current legislation but also of its evolutionary trend, being these disciplines in continuous and constant evolution. ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING At the end of the course, students will be able to understand the logic that governs the functioning of the markets and the profound interrelation between the framework of companies, products, their intermediation and supervision. JUDGMENT AUTONOMY Students develop a peripheral vision and a basic reconstructive skill of the frameworks examined, developing the ability to evaluate them also in a critical sense and in terms of consistency with the European legislation. COMMUNICATIVE SKILLS After attending the course, students acquire a legal language that, for the chosen university path, is of fundamental importance not only to have an expressive modality different from the other subjects studied but also to make an appropriate use of it also for the purpose of an adequate placement in a working environment. LEARNING SKILLS Language, expressive modalities, knowledge and critical scrutiny of the general and sector-specific disciplines covered by the course are the basis for the students to increase, on a much more solid basis, their ability to use them in the areas of competence
10626957 \| Financial econometrics [ECON-05/A] [ITA]	1st	2nd	9
Educational objectives Learning goals The aim of the course is to introduce students to the main methods of analysis and forecasting of the economic and financial time series. In particular, it covers i) Linear stochastic processes. Stationarity. Invertibility. Causality. ARMA processes. Identification, estimation, interpretation and forecasting. ii) Measurement and analysis of volatility. ARCH and GARCH models. Identification, estimation, interpretation and forecasting. Knowledge of the econometric theory for cross-section analysis, inference and probability theory is a prerequisite. Knowledge and understanding. After attending the course the students know and understand the main problems related to time series (for example: absence of stationarity) and the main methods to be used to solve such problems (for example: unit root tests). Applying knowledge and understanding. At the end of the course the students are able to formalize real problems in terms of linear regression models and to apply the methods specific to the discipline to solve them. They are also able to apply the methods to concrete situations and to interpret the results. Making judgements. Students develop a knowledge of the analytical properties of the presented methodologies and the ability to build programs for their implementation. They also learn to critically interpret the results obtained by applying the procedures to concrete situations. Communication skills. Students acquire the technical-scientific language of the discipline, which it must be used appropriately in both the intermediate and final written tests and in the oral tests. Communication skills are also developed through group activities. Learning skills. Students who pass the exam have learned a method of analysis that allows them to tackle the study of analytical properties in more complex modeling contexts in subsequent quantitative area teachings. They are also able to produce sound empirical analyzes and forecasts.
10626666 \| [STAT-03/A] [ITA]	1st	2nd	6
Educational objectives Learning goals The main learning goal is to learn the demographic techniques to study the dynamic characteristics of a population and to understand what is the role of a demographic variable – causes and effects – in the change of social and economic phenomena. The course provides skills for several fields of application, such as, for example, life insurance policies, social-security benefits, health-care and also financial planning. Knowledge and understanding Knowledge and understanding of main population trends and the dynamics of demographic phenomena are expected, together with adequate methodologies to learn about the importance of demographic dimension and related tecnnical practice. Applying knowledge and understanding At the end of the course the student will be able to build and analyse demographic indicators and instruments useful in the insurance sector, with particular reference to the construction of actual and future life tables and their use. The course provides all the tools, both theoretical and methodological, to make a population forecast and to read the results obtained correctly so that they can be used in the actuarial and financial fields. Making judgements Students will be able to evaluate the impact of the evolution of mortality, fertility and migration on the age structure of a population and, viceversa, be able to evaluate the influence that these structural changes will have in the mid and long term on the three components, mortality, fertility and migration. In particular, the course allows the students to choose the most suitable life tables for each specific field of application, especially the actuarial one. Communication skills Attending lessons and passing the final exam, the student acquires the demografic technical and scientific language , which is necessary to communicate results at work and generally speaking in the field of social security and assistance. Learning skills At the end of the course, students passing the exam will have learned the key role of the demographic dimension and will be able to apply the main quantitative tools to manage and analyse the actuarial eand financial processes. The competences acquired can be very useful to work in the field of social welfare plannning.
[N/D] [ITA]	1st	2nd	12
Educational objectives This course can be chosen by the student within the Sapienza courses as long as consistent with the curriculum.
Optional group: Curriculum Scienze Attuariali - Optional group F for 3 CFU/ ECTS
Optional group: Curriculum Scienze Attuariali - Optional group C for 12 CFU/ ECTS
10629845 \| Non-life insurance mathematics [STAT-04/A] [ITA]	2nd	1st	9
Educational objectives Learning goals. The main learning goal for students is the knowledge of principles, methods and techniques of non life insurance. Students must be able to apply the main actuarial models and to interpret the results of their use on real data. Knowledge and understanding. Students acquire knowledge and understanding of the most important problems of actuarial science for non life insurance (premium principles, technical proisions, ecc.) and of the main methods for solving these problems. Applying knowledge and understanding. After the attendance of this course, students will be able to formalize real problems and to apply appropriate actuarial models. They will also be able to apply actuarial models to real data and to interpret them. Making judgements. Students improve judgements skills by applying actuarial models to a wide range of non life insurance products. Their skills will be improved by using and comparing different methods to the same problems and by applying these methods to real data. Communication skills Students will acquire the scientific language of actuarial science for non life insurance, that will be used in written test. Communication skills will be enhanced also by group work. Learning skills. Students who pass the final exam will have acquired the methods and knowledge necessary to operate as non life actuaries, with a special regard for non life technical provition. These skills will allow them access to the State Examination to the Actuarial Profession.
10626429 \| Actuarial Techniques of Life Assurances [STAT-04/A] [ITA]	2nd	1st	9
Educational objectives GOALS The main objective of the course is to provide from an actuarial point of view the basic foundations of an insurance process and of the management of a life insurance company. More in detail, it wishes to allow the students to understand and proceed to: the analysis of technical aspects of the branches I,II,III,IV,V,VI , mentioned in the Legislative decree 7 September 2005, n.209: from the planning of the products and the structure of the ratings to the formation and quantification of needs and technical reserves; the development of an actuarial profile in the evaluation topics of the technical items contained in the budget; the development of product profitability and portfolios; the development of insurance activities; the solvency approach of a life insurance company according to the simplified standards of the corporate model; the propaedeutic risk oriented formulation of the rules of application and guide lines which are at the basis of the activity of the Actuary in charge and of the actuarial certification. Skill to acquire. The students, passed the course exam, will have a good knowledge of the topics described in the program and will have the capability to put what learnt into practice. More in detail, they will be able to proceed to the: technical-actuarial design of insurance policies belonging to the branches I,II,III,IV,V,VI; rating and quantification of the technical reserves; use of standard models during the insurance process and to the basic analysis of the management of a life-insurance company; application of evaluative methodologies to the profitabilty/value of life insurance products and portfolios, as well as to insurance activities (profit testing, embedded, actuarial appraisal value); technical analysis of the rules of application and of the guide lines to the activity of the Actuary in the life insurance sector.
10626792 \| Technique of social security pensions [STAT-04/A] [ITA]	2nd	2nd	9
Educational objectives GOALS The course provides fundamentals of actuarial and financial methods to manage supplementary pension schemes. Starting from the equilibrium models (of the collective type or individual, financial or actuarial) between contributions and benefits that may be adopted in a supplementary pension scheme, teaching topics deepens methodological actuarial and financial arguments to manage risks to which it is subjected a pension fund. SKILLS TO ACQUIRE The course, developed by means of tutorials and seminars, allows the student to the end of teaching activities, to acquire the knowledge on actuarial and financial methodologies to assess the effects due to the interaction of multiple sources of risk on a pension fund management.
10629121 \| Management and balance sheet of insurance companies [ECON-07/A] [ITA]	2nd	2nd	6
Educational objectives Learning goals The primary educational objective of the course is students' learning of the basics concerning the structure, the contents and the main evaluation methods of the balance sheet of life and non life insurance companies, with reference to the national legislation, the IAS / IFRS international accounting standards and the Solvency II project. Knowledge and understanding. At the end of the course the students know and understand the structure and elements of the financial statements of the insurance companies. Applying knowledge and understanding At the end of the course students are able to analyze a balance sheet of an insurance company. They are also able to understand the methods used to evaluate the main items of the financial statements. Making judgements. Students develop critical skills through the analysis of the balance sheet, also through the use of specific key performance indicators. Communication skills. The students, through the study and analysis of the financial statements, acquire the technical language of the discipline, which must be used appropriately in the final test. Communication skills are also developed through group activities and make students able to communicate with specialists and non-specialists. Learning skills. Students passing the exam have learned knowledge and method of analysis that allows them to deal with the topics developed during the course independently.
AAF1019 \| Final exam [N/D] [ITA]	2nd	2nd	21
Educational objectives To allow the student to the writing of an original text that represents the sum of the specialized knowledge achieved during the course of his study.
Optional group: Curriculum Scienze Attuariali - Optional group C for 12 CFU/ ECTS
Optional group: Curriculum Scienze Attuariali - Optional group F for 3 CFU/ ECTS

Lesson [SSD] [Language]	Year	Semester	CFU
AAF1235 \| LABORATORY OF STOCHASTIC PROCESSES [N/D] [ITA]	1st	1st	3
Educational objectives General goals The main goal of the course is to provide students with the main tools of the theory of random processes, with a focus on those stochastic models that are useful in quantitative finance and actuarial sciences. Knowledge and understanding By the end of the course, students will be able to recognize and understand the probabilistic models used in quantitative finance and actuarial sciences. Applying knowledge and understanding Students will be able to model complex phenomena by means of the theoretical concepts acquired during the lectures. In particular, the probabilistic tools studied during the course will enable the analysis and application of random processes to the financial asset management and insurance contracts. Making judgements By the end of the course, students will be able to critically analyze phenomena that evolve randomly over time. Furthermore, they will be able to choose the best suited models to the study of such complex systems. Communication skills Students will acquire the necessary communication skills useful for describing random phenomena through the language of mathematics and probability. These skills will be developed through an understanding of the intuitive aspects related to the mathematical tools underlying stochastic processes. Learning skills Students during the course will study the concepts necessary to deep the study of random processes and apply the main ideas of this theory to subsequent courses in finance and actuarial science.
AAF1149 \| [N/D] [ITA]	1st	2nd	3
Educational objectives The specific goal of these activities is to enable the students to merge their academic knowledge with professional skills. By facing practical and real problems, students develop judgement and communication skills.
AAF1301 \| Laboratory of Demography [N/D] [ITA]	2nd	1st	3
Educational objectives Learning goals The main learning goal is knowledge about potential of demographic variable and techniques in demography-related fields, with special attention to social security, health organization, business strategies. Knowledge and understanding The purpose of the laboratory is to make the students – who are looking at their future professional life - aware of importance of demographic skills, as regards issues and methods, to better evaluate impacts of population changes on markets (goods and services) and on society. Applying knowledge and understanding Lab of Demography offers skills at analyzing and interpreting relationship between demographic trends and the fundamental fields of human activity in society. Making judgements The lab aims at providing specific competences, particularly for population forecasts, use of population data sources, use of methods for causal analysis, making the students able and self-confident in selecting data and tecniques and in developing critical evaluation skills. Communication skills A group of frontal lessons are devoted to acquire basic skills for presentation and communication of knowledge and any results, allowing students to develop some communication skills, also thanks to study groups experience. Learning skills After passing the final test the student acquires substantial knowledge, specific skills and capacity to completely read and present population trend and phenomena.
AAF1528 \| Laboratory of actuarial techniques [N/D] [ITA]	2nd	1st	3
Educational objectives Learning goals The primary educational objective of the course is the students' learning of some actuarial models for the evaluation of insurance coverage typical of life and non life line of business through the IT application, the use of some dedicated software packages and software “ad hoc” implemented. Knowledge and understanding. After attending the course the students know theoretically and know how to deal with topics of particular interest in the actuarial technique of life and non life insurance. Applying knowledge and understanding. At the end of the course, students are able to construct and apply some evaluation models typical of the actuarial technique of life and non life insurance, using specific software as well as to interpret the results. Making judgements. Students develop critical skills through the application of different typical actuarial models in life and non life insurance, also using experience data. From the analysis of the results, the students learn a critical vision of the applied evaluation models. Communication skills. The students, through the study and practical application, acquire the technical language of the discipline, which must be used appropriately in the final test. Communication skills are also developed through group activities. Learning skills. Students passing the exam have learned knowledge and method of analysis that allows them to deal with the topics developed during the course independently.
AAF2054 \| MACHINE LEARNING FOR INSURANCE [N/D] [ITA]	2nd	1st	3
Educational objectives The primary educational objective of the course is the students' learning of the main machine learning techniques that can be used in insurance. This primary objective is achieved through the IT application with the use of open source software.

Lesson [SSD] [Language]	Year	Semester	CFU
10629321 \| MATHEMATICS FOR INSURANCE [STAT-04/A] [ITA]	1st	2nd	6
Educational objectives Learning goals. The main learning goal for students is the knowledge of principles and methods of actuarial mathematics, both of life and non life insurance. Students must be able to apply the main actuarial models and to interpret the results of their use on real data. Knowledge and understanding. Students acquire knowledge and understanding of the most important problems of actuarial mathematics (probabilistic models, premium principles, reserves, ecc.) and of the main methods for solving these problems (variance principle, chain ladder method, Homans formula, ecc.). Applying knowledge and understanding. After the attendance of this course, students will be able to formalize real problems and to apply appropriate actuarial models. They will also be able to apply actuarial models to real data and to interpret them. Making judgements. Students improve judgements skills by applying actuarial models to a wide range of insurance products. Their skills will be improved by using and comparing different methods to the same problems and by applying these methods to real data. Communication skills Students will acquire the scientific language of Actuarial mathematics, that will be used in written and oral tests. Communication skills will be enhanced also by group work. Learning skills. Students will acquire the fundamental knowledge needed to study formal actuarial properties of more complex models in more advanced classes.
10625989 \| Monte Carlo Methods in finance and insurance [STAT-04/A] [ENG]	1st	2nd	6
Educational objectives Learning goals The course aims to provide the foundations for the application of Monte Carlo techniques in finance and insurance, both for the valuation of contracts and for the measurement of risks, and to develop the critical ability for the interpretation of the results. Knowledge and understanding After attending the course the students have learned the principles of the Monte Carlo methods, they are able to apply the appropriate techniques to different financial and actuarial problems and to estimate the accuracy of the results obtained. Applying knowledge and understanding After attending the course the students are able to use the Monte Carlo method the solve problems of estimation and of error estimation. Making judgements Students develop critical skills by comparing the use of Monte Carlo methods applied to problems of increasing complexity. Communication skills The students, through the study of theory and practical examples, acquire the technical-scientific language of the discipline, which must be opportunely used also in the final test. Learning skills Students who pass the exam have learned a method of analysis that allows them to deal with more complex problems and a larger set of risks.
10629797 \| Stochastic processes for finance and insurance [MATH-03/B] [ITA]	1st	2nd	6
Educational objectives General goals The main goal of the course is to introduce advanced random processes and probabilistic tools that are particularly useful in quantitative finance and actuarial sciences. Knowledge and understanding By the end of the course, students will be able to understand the meaning of random patterns (e.g., with jumps) arising in the study of financial and insurance topics. Applying knowledge and understanding Students will acquire the skills necessary to model complex phenomena through the theoretical concepts explored in depth during the lectures. In particular, the advanced stochastic analysis tools studied during the course will enable students to address some actuarial and financial issues. Making judgements By the end of the course, students will be able to critically analyze phenomena that evolve randomly over time and are subject to random shocks. Furthermore, students will develop the sensitivity necessary to choose models best suited to the study of such complex systems. Communication skills Students will develop communication skills useful for describing random phenomena through the language of mathematics and probability. These skills will emerge through understanding the intuitive aspects related to the mathematical tools underlying stochastic processes. Learning skills Students during the course will study stochastic concepts and methods that will enable them to understand subsequent courses in finance and actuarial sciences.
10629405 \| Forecasting models [STAT-01/A] [ITA]	2nd	1st	6
Educational objectives Learning goals. Main goal is the ability to conduct a statistically correct analysis and a forecasting exercise in all cases where time a fundamental feature of the analysed data. Knowledge and understanding. Demonstrate knowledge and understanding ability that extend those typical of the course of time series of the first degree, and allow also to develop original forecast proposal, on integrating different methodologies. Applying knowledge and understanding. Solving complex problem related to the time dynamics of several phenomena measured on different scales and with different methods. Making judgements. Ability to integrate knowledge and perform analysis of complex phenomena integrating different methodologies, also in presence of limited, incomplete or biased information. Communication skills. Communicate the results of a deep statistical analysis, illustrating the main steps and motivation also to non-specialst audience. Learning skills. To study in a self-managed and autonomous fashion.
10625912 \| Economy and finance for insurance [STAT-04/A] [ITA]	2nd	2nd	6
Educational objectives Obiettivi – Nel corso si trattano i temi fondamentali del nuovo stile di governance dell’impresa di assicurazione, come regolamentato dalla Direttiva europea “Solvency II”. Sono affrontate le problematiche tecniche di calcolo delle grandezze caratteristiche dell’“economic balance sheet”, e i processi di organizzazione algoritmica. Il corso ha l’obiettivo di fornire competenze per le figure professionali richieste dalla nuova governance: per il risk management, per l’actuarial funcion, per l’auditing.

Quantitative finance

Lesson [SSD] [Language]	Year	Semester	CFU
10627887 \| Statistical methods for finance and insurance [STAT-01/A] [ITA]	1st	1st	9
Educational objectives Learning goals The primary aim of the course is the students' knowledge of the most relevant statistical methods for financial and insurance data. Knowledge and understanding. Knowledge of the most applied statistical techniques in the domains of inference, time series and dependence for for financial and insurance data. Applying knowledge and understanding. Ability to formalize real problems in the fields of finance and insurance in statistical terms and to solve them by applying the corresponding statistical methods. Making judgements. Ability to apply statistical methods and to evaluate the reliability of the results obtained by analyzing real financial and insurance data. Communication skills. By studying and by examples, learning and acquiring technical and scientific language in the statistical domain to be used properly in the final evaluation. Learning skills. Students passing the exams acquire the knowledge for facing issues concerning finance and insurance, in courses devoted to finance and insurance, by means of statistical methods.
10626938 \| Mathematical Models For Financial Markets [STAT-04/A] [ITA]	1st	1st	9
Educational objectives Learning goals The course deals with the topics essential for acting in the financial market. It has the goal of providing the fundamental notions for the formalization and valuation of financial derivatives and for risk management. Knowledge and understanding After attending the course the students are familiar with the principles of valuation of derivative contracts and with some of the main stochastic models for the evaluation of equity, interest rate and credit risk. They are able to appreciate the role of modeling hypotheses in the evaluation process, also from the point of view of numerical complexity. Applying knowledge and understanding After attending the course the students are able to formalize, in a stochastic environment, the problems of pricing and measuring risks of financial contracts. Making judgements Students develop critical skills through the comparison of different financial hypotheses applied to problems of increasing complexity. Communication skills Students, through the study of theory and practical examples, acquire the technical-scientific language of the discipline, which must be used appropriately in the oral examination. Learning skills Students passing the exam have learned a method of analysis that allows them to tackle financial problems involving more complex financial instruments and a broader sets of risks.
10628881 \| Insurance and banking law [GIUR-03/A] [ITA]	1st	1st	6
Educational objectives GENERAL OBJECTIVES The course intends to introduce students to the study of the operational rules of financial markets, with particular regard to insurance. Students must not only learn the basics but also analyse them critically, especially with regard to the sound ratio of their discipline. KNOWLEDGE AND UNDERSTANDING SKILLS After attending the course, the students will know and understand how to deal with the study not only of current legislation but also of its evolutionary trend, being these disciplines in continuous and constant evolution. ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING At the end of the course, students will be able to understand the logic that governs the functioning of the markets and the profound interrelation between the framework of companies, products, their intermediation and supervision. JUDGMENT AUTONOMY Students develop a peripheral vision and a basic reconstructive skill of the frameworks examined, developing the ability to evaluate them also in a critical sense and in terms of consistency with the European legislation. COMMUNICATIVE SKILLS After attending the course, students acquire a legal language that, for the chosen university path, is of fundamental importance not only to have an expressive modality different from the other subjects studied but also to make an appropriate use of it also for the purpose of an adequate placement in a working environment. LEARNING SKILLS Language, expressive modalities, knowledge and critical scrutiny of the general and sector-specific disciplines covered by the course are the basis for the students to increase, on a much more solid basis, their ability to use them in the areas of competence
10626957 \| Financial econometrics [ECON-05/A] [ITA]	1st	2nd	9
Educational objectives Learning goals The aim of the course is to introduce students to the main methods of analysis and forecasting of the economic and financial time series. In particular, it covers i) Linear stochastic processes. Stationarity. Invertibility. Causality. ARMA processes. Identification, estimation, interpretation and forecasting. ii) Measurement and analysis of volatility. ARCH and GARCH models. Identification, estimation, interpretation and forecasting. Knowledge of the econometric theory for cross-section analysis, inference and probability theory is a prerequisite. Knowledge and understanding. After attending the course the students know and understand the main problems related to time series (for example: absence of stationarity) and the main methods to be used to solve such problems (for example: unit root tests). Applying knowledge and understanding. At the end of the course the students are able to formalize real problems in terms of linear regression models and to apply the methods specific to the discipline to solve them. They are also able to apply the methods to concrete situations and to interpret the results. Making judgements. Students develop a knowledge of the analytical properties of the presented methodologies and the ability to build programs for their implementation. They also learn to critically interpret the results obtained by applying the procedures to concrete situations. Communication skills. Students acquire the technical-scientific language of the discipline, which it must be used appropriately in both the intermediate and final written tests and in the oral tests. Communication skills are also developed through group activities. Learning skills. Students who pass the exam have learned a method of analysis that allows them to tackle the study of analytical properties in more complex modeling contexts in subsequent quantitative area teachings. They are also able to produce sound empirical analyzes and forecasts.
10627831 \| International monetary economics [ECON-01/A] [ENG]	1st	2nd	9
Educational objectives Learning goals Working knowledge of the main models of international economics and international finance. Knowledge and understanding. Upon successful completion of the course, students will be able to analyse actual economic problems in terms of competing theories and models. Applying knowledge and understanding. Upon successful completion of the course, students will be able to understand the explicit and implicit hypotheses informing the main economic policy proposals in the current debate. Making judgements. The course is explicitly based on the principle of methodological and theoretical pluralism. Students will be introduced to at least two competing models for each economic problem considered, and will understand the criteria with which to personally choose their favorite interpretation. Communication skills. Through study and hands-on sessions, students will become proficient in the jargon and technical language of the discipline, which they must use in both written and oral examinations. Learning skills. Students that successfully complete the course will have learnt a method of analysis that will allow them to tackle and understand the main economic issues of today, both in subsequent economic courses and in the fruition and participation to the public debate.
[N/D] [ITA]	1st	2nd	12
Educational objectives This course can be chosen by the student within the Sapienza courses as long as consistent with the curriculum.
Optional group: Curriculum Quantitative Finance - Optional group F for 3 CFU/ ECTS
Optional group: Curriculum Quantitative Finance - Optional group C for 12 CFU/ ECTS
10625905 \| Asset pricing [STAT-04/A] [ENG]	2nd	1st	9
Educational objectives Learning goals To provide an understanding of derivatives contracts and the models used to price them. The arbitrage theorem and the modern financial theory represent the building blocks for the model development and understanding Knowledge and understanding It is expected the learning of the basic elements of classical mathematical finance to understand how financial markets work and how complex financial insruments can be assessed. The ability of the autonomous use of the financial techniques in several activities and works in this sector are also expected, as well as making autonomous judgements ability, learning and communication abilities. Applying knowledge and understanding Each theoretical concept will be applied to real cases. Students will be assessed according to their ability to solve specific problems. Making judgements Each student will be required to download real market data and validate the pricing models used for option contracts or futures and he will be able to validate his/her ability to do so. Communication skills Each student will be required to present the application of studied methodologies to solve a real problem. Learning skills. The learned concepts will be tested having each student to undertake a final exam.
10629405 \| Forecasting models [STAT-01/A] [ITA]	2nd	1st	6
Educational objectives Learning goals. Main goal is the ability to conduct a statistically correct analysis and a forecasting exercise in all cases where time a fundamental feature of the analysed data. Knowledge and understanding. Demonstrate knowledge and understanding ability that extend those typical of the course of time series of the first degree, and allow also to develop original forecast proposal, on integrating different methodologies. Applying knowledge and understanding. Solving complex problem related to the time dynamics of several phenomena measured on different scales and with different methods. Making judgements. Ability to integrate knowledge and perform analysis of complex phenomena integrating different methodologies, also in presence of limited, incomplete or biased information. Communication skills. Communicate the results of a deep statistical analysis, illustrating the main steps and motivation also to non-specialst audience. Learning skills. To study in a self-managed and autonomous fashion.
10627024 \| Financial risk management [STAT-04/A] [ENG]	2nd	2nd	9
Educational objectives Learning goals The aim of the course is to introduce students to the main methods of analysis and forecasting of the economic and financial time series. In particular, it covers i) Linear stochastic processes. Stationarity. Invertibility. Causality. ARMA processes. Identification, estimation, interpretation and forecasting. ii) Measurement and analysis of volatility. ARCH and GARCH models. Identification, estimation, interpretation and forecasting. Knowledge of the econometric theory for cross-section analysis, inference and probability theory is a prerequisite. Knowledge and understanding. After attending the course the students know and understand the main problems related to time series (for example: absence of stationarity) and the main methods to be used to solve such problems (for example: unit root tests). Applying knowledge and understanding. At the end of the course the students are able to formalize real problems in terms of linear regression models and to apply the methods specific to the discipline to solve them. They are also able to apply the methods to concrete situations and to interpret the results. Making judgements. Students develop a knowledge of the analytical properties of the presented methodologies and the ability to build programs for their implementation. They also learn to critically interpret the results obtained by applying the procedures to concrete situations. Communication skills. Students acquire the technical-scientific language of the discipline, which it must be used appropriately in both the intermediate and final written tests and in the oral tests. Communication skills are also developed through group activities. Learning skills. Students who pass the exam have learned a method of analysis that allows them to tackle the study of analytical properties in more complex modeling contexts in subsequent quantitative area teachings. They are also able to produce sound empirical analyzes and forecasts.
10628033 \| MULTIPLE TIME SERIES MODELLING [STAT-02/A] [ENG]	2nd	2nd	6
Educational objectives Learning goals The main goal is acquiring advanced modelling techniques for mutivariate economic data. Students are expected to understand the theoretical foundations of the methods studied and to apply them to real datasets. Knowledge and understanding The focus of the course will on the Vector Autoregressive (VAR) model in stationary and non stationary settings, using both asymptotic and simulation (bootstrap) inference Applying knowledge and understanding After the course students will be able to specify a VAR model, evaluate if is adequate to the dataset of interest , use for estimating causal relationship and formatulate forecasts Making judgements Learning how to judging the adequacy of the models and assessing the uncertainty of the estimated relationships and forecasts will be an essential part of the course Communication skills Learning to communicate the results of the estimation process both in oral and written form will be an essential part of the course Learning skills The models object of the course are essential parts of the most advanced and complex models used in quantitative economic analysis, which the students will then be able to tackle."
AAF1019 \| Final exam [N/D] [ITA]	2nd	2nd	21
Educational objectives To allow the student to the writing of an original text that represents the sum of the specialized knowledge achieved during the course of his study.
Optional group: Curriculum Quantitative Finance - Optional group C for 12 CFU/ ECTS
Optional group: Curriculum Quantitative Finance - Optional group F for 3 CFU/ ECTS

Lesson [SSD] [Language]	Year	Semester	CFU
AAF1235 \| LABORATORY OF STOCHASTIC PROCESSES [N/D] [ITA]	1st	1st	3
Educational objectives General goals The main goal of the course is to provide students with the main tools of the theory of random processes, with a focus on those stochastic models that are useful in quantitative finance and actuarial sciences. Knowledge and understanding By the end of the course, students will be able to recognize and understand the probabilistic models used in quantitative finance and actuarial sciences. Applying knowledge and understanding Students will be able to model complex phenomena by means of the theoretical concepts acquired during the lectures. In particular, the probabilistic tools studied during the course will enable the analysis and application of random processes to the financial asset management and insurance contracts. Making judgements By the end of the course, students will be able to critically analyze phenomena that evolve randomly over time. Furthermore, they will be able to choose the best suited models to the study of such complex systems. Communication skills Students will acquire the necessary communication skills useful for describing random phenomena through the language of mathematics and probability. These skills will be developed through an understanding of the intuitive aspects related to the mathematical tools underlying stochastic processes. Learning skills Students during the course will study the concepts necessary to deep the study of random processes and apply the main ideas of this theory to subsequent courses in finance and actuarial science.
AAF1149 \| [N/D] [ITA]	1st	2nd	3
Educational objectives The specific goal of these activities is to enable the students to merge their academic knowledge with professional skills. By facing practical and real problems, students develop judgement and communication skills.
AAF2432 \| Economics reading seminars [N/D] [ENG]	2nd	1st	3
Educational objectives Learning goals. Aim of the course is to allow students to broaden their knowledge of economics, sociology, and other social sciences in an interdisciplinary way. Knowledge and understanding. Historical perspective and awareness of the existence of different interpretative positions in the context of social sciences. Applying knowledge and understanding. At the end of the course students will be able to deal with different models in a critical way. Making judgements. Students will develop critical skills through different theoretical approaches. Communication skills. Students, through the study, acquire the language of different disciplines, which must be appropriately used both in written and oral exams. Learning skills. Students who pass the exam have learned a method of analysis that allows them to tackle the study of more complex models.
AAF1544 \| Laboratory of Stochastic Processes [N/D] [ENG]	2nd	1st	3
Educational objectives Learning goals. General learning targets: The course is organised as a series of classes where the students will have the possibility to solve and discuss the solutions of a series of advanced exercises on the theory of stochastic processes. Knowledge and understanding. At the end of the course the students will acquire the ability to solve autonomously simple and more advanced exercises on the theory of stochastic processes. Applying knowledge and understanding. During the course the students will exercise the ability to grasp and formalize, in the language of stochastic processes, phenomena that evolve in time and space and to solve simple applied problems in new environments and broader contexts. Making judgements At the end of the course the students will have the tools to evaluate critically and choose between different stochastic models to model phenomena that evolve in time and space. Communication skills. The students will exercise the intuition and the communication skills necessary to describe phenomena in the mathematical language of stochastic processes. In particular the student will acquire familiarity with the main ideas that are behind the stochastic model, e.g., the ideas of Markovianity, transience, recurrence, equilibrium, stationarity, long and short-time behaviour. Learning skills. The students will acquire autonomy in studying more advanced theoretical aspects of stochastic processes and in applying the main ideas of stochastic processes to the subsequent studies in the area of statistics and finance.
AAF2054 \| MACHINE LEARNING FOR INSURANCE [N/D] [ITA]	2nd	1st	3
Educational objectives The primary educational objective of the course is the students' learning of the main machine learning techniques that can be used in insurance. This primary objective is achieved through the IT application with the use of open source software.
AAF1881 \| Laboratory of quantitative finance [N/D] [ENG]	2nd	2nd	3
Educational objectives Learning goals The laboratory of Quantitative Finance recalls and deepens the implementation of the topics typical of the course of Quantitative Finance: Futures, forwards, options. The binomial model, Brownian motion. The model of Black and Scholes. The Greeks. Knowledge and understanding. The student needs knowledge on Quantitative finance and programming. Applying knowledge and understanding. At the end of the course, the student will be able to apply the knowledge acquired in the theoretical classes. Making judgements. The student will be able to evaluate the coherence of the results and to perform comparisons. Communication skills. The student will be able to communicate the results through a technical language. Learning skills. The student will be able to perform autonomously numerical evaluation of financial products.

Lesson [SSD] [Language]	Year	Semester	CFU
10625989 \| Monte Carlo Methods in finance and insurance [STAT-04/A] [ENG]	1st	2nd	6
Educational objectives Learning goals The course aims to provide the foundations for the application of Monte Carlo techniques in finance and insurance, both for the valuation of contracts and for the measurement of risks, and to develop the critical ability for the interpretation of the results. Knowledge and understanding After attending the course the students have learned the principles of the Monte Carlo methods, they are able to apply the appropriate techniques to different financial and actuarial problems and to estimate the accuracy of the results obtained. Applying knowledge and understanding After attending the course the students are able to use the Monte Carlo method the solve problems of estimation and of error estimation. Making judgements Students develop critical skills by comparing the use of Monte Carlo methods applied to problems of increasing complexity. Communication skills The students, through the study of theory and practical examples, acquire the technical-scientific language of the discipline, which must be opportunely used also in the final test. Learning skills Students who pass the exam have learned a method of analysis that allows them to deal with more complex problems and a larger set of risks.
10627241 \| Panel data modelling [STAT-02/A] [ENG]	1st	2nd	6
Educational objectives General Targets: Prior educational teaching concern is the students’ understanding of the main (Economic Statistics Modeling) problems and methods for Panel Data making use of parametric estimation. Here the empirical focus is on individuals represented by Decisional Making Units (DMU). More specifically, these are banks typically involved in the European (and also international) banking system. The course will focus on managerial problems of these firms by studying equations such as cost (mostly) and profit functions which are relevant to asses on the Efficiency of banks. Furthermore, students should know both how to solve analytical problems, in order to apply the appropriate methodology, and to interpret results obtained from empirical applications to actual data. Specific Targets: a) Knowledge and capability in understanding. After attending the course, students know and understand main problems of Panel Data. In particular, the course will account for the logic for building empirical models, related to the underlying economic theory (and the consequent subdivisions in endogenous and exogenous variables), with one or more equations in order to evaluate the degree of efficiency of a typical Decisional Making Unit (here the bank and possibly the insurance company). We will study the main estimation methods of Panel Data for solving efficiency problems pertaining a firm traditionally operating in the private sector. b) Capability of applying knowledge and comprehension At the end of the course students are able to formalize and solve problems by means of specific methods as well as treating fundamental models of Panel Data to answer questions on the Efficiency and Productivity Analysis for the banking system. Finally, students will be able to apply the methods studied to real data and interpret results correctly also from a theoretical point of view. c) Autonomy in assessment. Students develop analytical skills and capacity of facing different alternative approaches for solving actual empirical problems. d) Communication ability. Students learn technical language which is appropriate for the subject studied and that will be used at the oral and written exam, by means of practical exercises. e) Learning capacity. Students passing the exam are capable to extend the methodology studied also to other fields and derive conclusions.
10629797 \| Stochastic processes for finance and insurance [MATH-03/B] [ITA]	1st	2nd	6
Educational objectives General goals The main goal of the course is to introduce advanced random processes and probabilistic tools that are particularly useful in quantitative finance and actuarial sciences. Knowledge and understanding By the end of the course, students will be able to understand the meaning of random patterns (e.g., with jumps) arising in the study of financial and insurance topics. Applying knowledge and understanding Students will acquire the skills necessary to model complex phenomena through the theoretical concepts explored in depth during the lectures. In particular, the advanced stochastic analysis tools studied during the course will enable students to address some actuarial and financial issues. Making judgements By the end of the course, students will be able to critically analyze phenomena that evolve randomly over time and are subject to random shocks. Furthermore, students will develop the sensitivity necessary to choose models best suited to the study of such complex systems. Communication skills Students will develop communication skills useful for describing random phenomena through the language of mathematics and probability. These skills will emerge through understanding the intuitive aspects related to the mathematical tools underlying stochastic processes. Learning skills Students during the course will study stochastic concepts and methods that will enable them to understand subsequent courses in finance and actuarial sciences.
10632242 \| COMPLEX NETWORKS IN FINANCE [STAT-04/A] [ENG]	2nd	1st	6
Educational objectives Knowledge and understanding By the end of the course, the student is familiar with the fundamental concepts of the theory of complex systems and the main methodologies for financial system analysis. Understand the structural characteristics of the networks, the main graph generation models, the centralization, assortment, modularization, and resilience measures, as well as the dynamic processes that develop on the networks, with special reference to the diffusion of systemic risk, the spread of financial crises, and the networks of correlation between financial data. Applying knowledge and understanding The student gains the ability to clearly and rigorously communicate models, methodology, and results related to financial research using appropriate technical language and graphic and quantitative support. Additionally, it is capable of presenting the findings of its own analysis and critically discussing scholarly articles. Making judgements The student develops the ability to choose the best tools for analyzing complex financial problems, evaluate the limitations of adopted models, and critically interpret the results obtained. They are capable of making independent judgments about how the structure of reti affects market stability and the effectiveness of the methods used. Communication skills The student gains the ability to clearly and rigorously communicate models, methodology, and results related to financial research using appropriate technical language and graphic and quantitative support. Additionally, they are capable of critically discussing scientific articles and presenting the findings of their own analyses both orally and in writing. Learning skills By consulting international scientific literature and using specialized software for financial data analysis, the student develops the skills necessary to independently approach advanced topics in the field of complex data, quantitative finance, and data science.
10632241 \| EMPIRICAL ECONOMICS AND FINANCIAL DECISIONS [ECON-01/A] [ENG]	2nd	2nd	6
Educational objectives Learning goals The primary learning goal of this course is that of exposing students to the body of econometric techniques that are customised to economics applications. The aim of the course is to review this body of techniques, to demonstrate their use in hands-on style, drawing on as wide a range of example as possible, and to interpret each set of results in ways that are most useful to read and represent economic phenomena. Knowledge and understanding. The course is supposed to broaden students' knowledge of the various econometric techniques that appear in the economics literature, their properties and the way these are applied to data in order to verify economic theory. Applying knowledge and understanding. Upon successful completion of the course, students will be able to carry out a wide range of tasks in empirical economics, such as recognising the most suitable approaches to analyse the data at hand in order to capture and model its regularities, and intelligibly convey its messages to both economists and broader audiences. Making judgements. The course develops in a way to spurs students on researching empirical evidence of competing economic theories by respecting the nature of convenient data. Communication skills. Through study and hands-on sessions, students will acquire the terminology characterising the discipline, which they are required to use in both written and oral dissemination. Learning skills. Students who complete the course successfully will be acquainted with a method of analysis enabling them to endeavour the main economic issues from an empirical point of view.

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Actuarial and Financial Sciences

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Curriculum(s) for 2026 - Actuarial and Financial Sciences (33638)