Actuarial Mathematics PROF. GIAN PAOLO CLEMENTE

PROPERTY-CASUALTY MODULE (PROPERTY-CASUALTY INSURANCE)

COURSE AIMS The aim of the course is to analyse main technical aspect regarding non-life insur- ance focusing on the theory, methods and empirical implementation of actuarial models. Starting from the main forms of insurance cover, the program will focus on the valuation of premiums and technical reserves for short-term Property and Casualty Insurance. In particular, actuarial models for aggregate claims amounts are discussed by modelling, through empirical and probabilistic approaches, separ- ately the two components, namely claim frequency and claim severity. Moreover the course covers the basic methodology used in experience rating system (both a priori and a posteriori premium rating) and the valuation of safety and expenses loadings. Different reinsurance treaties will be described by analysing the effect on the aggregate claim amount and pricing. Finally, a historical review and a descrip- tion of the actual solvency system will be accomplished. At the end of the course, students will be able to calculate premiums for non-life insurance contracts and to assess the balance in order to ensure a technical and capital equilibrium.

COURSE CONTENT Prerequisites Before entering the course, the student should: – be able to use continuously discrete and continuous random variables; – know the concepts of probability function, density function and distribution functions; – be able to obtain main moments and cumulants of a probability distribution; – be familiar with the main discrete and continuous probability distributions. Course outline and detailed learning goals Non-Life insurance covers and main Italian market statistics At the end of this section of the course the student will: – be able to define the basic short-term contracts in non-life insurance; – know the main non-life lines of business; – be able to understand the main characteristics of the Italian insurance mar- ket. Calculation of risk premium At the end of this section of the course the student will be able to: – describe the random variable aggregate claim amount; – construct appropriate models for short term insurance contracts in terms of numbers of claims and amount of individual claims; – obtain a fair premium and a fair rate for non-life contracts with both probab- ilistic and empirical approach; – evaluate risk premium by considering policy limits and deductibles; – adjust risk premium in order to take into account the effect of inflation, changes in policy limits and in technical assumptions. Calculation of gross premium At the end of this section of the course the student will be able to: – understand the need of safety loading; – evaluate the safety loading by different criteria; – understand the main source of costs in non-life insurance; – evaluate expenses loading; – obtain a gross premium. Premium customization At the end of this section of the course the student will be able to: – describe the basic methodology used in rating general insurance business; – implement a priori premium customization; – understand a simple experience rating system; – adjust rate premiums by using credibility theory. Technical reserves At the end of this section of the course the student will: – know non-life technical provisions; – be able to evaluate the unearned and total premium reserve; – be able to construct and understand a run-off triangle by the accounting re- ports; – be able to understand the claims reserve, the IBNR reserve and a valuation case by case of outstanding claims reserve. Deterministic methods for claim reserves At the end of this section of the course the student will be able to: – evaluate claims reserve using the paid chain-ladder method; – evaluate claims reserve using the Fisher-Lange method. Risk retention and reinsurance methods At the end of this section of the course the student will: – know different form of reinsurance agreements; – be able to compare different treaties; – be able to investigate the methods used to choose reinsurance cover and its effects on the equilibrium of an insurer. Solvency At the end of this section of the course the student will: – know a historical review of solvency system; – be able to evaluate the minimum solvency margin and solvency ratio; – be able to understand main limits of actual solvency system.

READING LIST

N. SAVELLI-G.P. CLEMENTE, Lezioni di Matematica Attuariale delle Assicurazioni Danni, Serie Materiale e Documenti, pag. 1-184, EduCatt, Milano, 2014. In-depth study Readings/Lecture notes will be indicated during the course in relation to classroom interventions by experts in the field.

TEACHING METHOD Lectures.

ASSESSMENT METHOD Oral examination.

NOTES Further information can be found on the lecturer's webpage at http://docenti.unicatt.it/web/searchByName.do?language=ENG or on the Faculty notice board.