Finance and insurance

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.