THEORY OF RISK

Course objectives

Learning goals. The main objective of this course is to provide the knowledge a life actuary requires to operate accordingly to the Solvency II directive. It will teach students to understand valuation techniques for with profit, unit linked, and index linked policies; methods of life best-estimate, SCR, and cost-of-capital calculation according to the Solvency II directive. Knowledge and understanding At the end of the course, students will know and understand the principles of life market-consistent evaluation (best estimate). They will be able to comprehend the standard formula SCR calculation criteria. They will be familiar with the main validation tests. They will understand profit test reports. Applying knowledge and understanding At the end of the course, students will have acquired the ability to apply best estimate and SCR calculation methods to real cases. Additionally, they will be able to evaluate with profit policies, in an Asset Liabilities Management setting, using segregated fund accounting rules. They will know how to realize the accuracy, robustness, market consistency, and "martingale" tests required by regulation for the economic scenarios generator. Using these abilities, they will plan profit test reports. Making judgements Students will be able to critically interpret the outcomes of models, by varying the contractual parameters and/or the model parameters. Communication skills. The students acquire the knowledge of industry jargon and of the relevant linguistic correspondences (Italian-English). Learning skills. Students who pass the final exam will have acquired the methods and knowledge necessary to operate as life actuaries, with a special regard for life technical provition and SCR according to the Solvency II directive. These skills will allow them access to the State Examination to the Actuarial Profession.

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FABIO BAIONE Lecturers' profile

Program - Frequency - Exams

Course program
The lecturers are divided into the following main contents: Part 1: Introduction to Risk Theory: from origins to Enterprise Risk Management. Fundamentals of Quantitative Risk Management (approximately 4 hours). Topics: Definition of Risk. Review of the concepts of deferment and uncertainty. Main frameworks of international and national principles and reference regulations. Part 2: Review of the main discrete and absolutely continuous distributions for non-life insurance assessment and effects of risk limitation (approximately 12 hours). Topics: Density functions, distribution functions, moment generating functions, probability generating functions, and cumulants. Synthetic indices of a distribution: moments, quantiles, skewness, and kurtosis. Risk limitations and reduction: absolute and relative deductibles, maximums, inflation, and co-insurance. Part 3: Aggregate risk models (approximately 12 hours). Topics: Total claim distribution: Individual vs. Collective risk Model. Mixed distributions: the Poisson Gamma distribution. Approximation formulas for cumulative claims cost, Tweedie distribution. Part 4: Risk assessment models (approximately 8 hours). Topics: A first example of premium calculation. Principles of premium calculation: individual and collective premium. Premium calculation through statistical observation: Risk rating and Experience Rating. Bühlmann's credibility theory. Part 5: Ruin and risk control (approximately 12 hours). Topics: Probability of ruin. An introductory example: the probability of ruin in an exercise. Player ruin: fair game and unfair game. The free reserve process and probability of ruin; the Cramer-Lundberg-de Finetti theorem. Part 6: Company stability and reinsurance (approximately 4 hours). Topics: Logic of reinsurance and the “problema dei pieni assoulti e relativi". "Pieni" and portfolio selection theory.
Prerequisites
The content of the course requires a basic understanding of probability calculus (random variables, probability distributions, moments) and actuarial mathematics (random financial operations, life, and non-life insurance) as well as a good knowledge of statistics and some basics of financial mathematics and economic logic. Therefore, it is considered a prerequisite to have acquired some of the notions through examinations in the courses of Statistics, Probability, and Actuarial Mathematics.
Books
Lecture notes
Frequency
Classroom attendance is not mandatory but is strongly recommended.
Exam mode
To pass the exam, an oral test on the theoretical topics covered in the program is scheduled. This test assesses the ability to reason and analyze rigorously on the course subjects, as well as language proficiency and communication skills.
Bibliography
- Loss Data Analytics, aa.vv. https://ewfrees.github.io/Loss-Data-Analytics/ - Loss Models: from Data to Decisions, Klugman S.A., H.H. Panjer e G.E. Willmot (3rd Editon o sup), Wiley Series in Probability and Statistics.
  • Lesson code1017270
  • Academic year2024/2025
  • CourseStatistics, Economics, Finance and Insurance
  • CurriculumFinanza e assicurazioni
  • Year3rd year
  • Semester2nd semester
  • SSDSECS-S/06
  • CFU6
  • Subject areaInformatico-matematico applicato