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Actuarial Mathematics (Damage Insurance) PROF. NINO SAVELLI COURSE AIMS To deal rigorously and systematically with the most significant decision-making problems regarding damage insurance. The course covers the following subjects: the main forms of insurance cover against damage, calculation of the fair premium, the need for loading for contingencies, expense loadings and calculation of rate premiums, a priori premium customization, a posteriori premium customization and the bonus-malus system, technical reserves, reinsurance and solvency. Besides the theory lectures, the course includes a few practice sessions. At the end of the course, participants will be able to calculate risk and rate premiums for damage insurance cover, and be familiar with the main problems linked with providing damage insurance to ensure correct technical and capital equilibrium. COURSE CONTENT Things students should know before starting the course Before starting, the student should: – be familiar with the concepts of discrete and continuous random variables; – be familiar with the concepts of probability function, density function and distribution functions; – be familiar with the concepts of mean, variance and asymmetry, and methods for calculating moments; – be familiar with the main discrete and continuous probability distributions. Things students will learn during the course Kinds of insurance cover against damage and the main Italian market statistics Once the subject has been covered, students will: – be familiar with the main kinds of insurance cover in damage insurance; – be familiar with the main branches of insurance; – be familiar with the main characteristics of the Italian insurance market. Calculation of risk premium Once the subject has been covered, students will: – be able to calculate the risk premium of an insurance contract with an empirical approach; – be able to measure the risk premium with a theoretical approach; – be familiar with the characteristics of the two main risk premium variables: frequency and mean cost; – be able to calculate the risk premium with contract constraints: limit of liability, threshold and uninsured percentage; – be able to adjust the premium according to inflation. Forming the rate premium Once the subject has been covered, students will: – understand and be able to explain the need for loading for contingencies; – be able to use different methods to calculate loading for contingencies; – be familiar with the sources of the costs which affect the management of a damage insurance contract; – be able to calculate suitable expense loadings; – be able to calculate the rate premium. Premium customization Once the subject has been covered, students will: – be ale to implement suitable a priori premium customization; – be familiar with the Italian bonus-malus system, and assess its benefits and the critical points of its application; – be ale to implement suitable a posteriori premium customization; – be able to adjust the premium using the credibility theory. Risk retention and reinsurance methods Once the subject has been covered, students will: – be familiar with the characteristics of a reinsurance agreement; – be able to compare different kinds of cover; – be familiar with the methods used to calculate reinsurance premiums; – be able to investigate the methods used to choose reinsurance cover and its effects on the equilibrium of a firm. Technical reserves Once the subject has been covered, students will: – be familiar with the main kinds of technical reserve found in damage insurance; – be able to calculate the premium reserve; – be familiar with the characteristics of the loss reserve; – be familiar with and be able to use a run-off triangle. Solvency Once the subject has been covered, students will: – be familiar with the concept of solvency; – be familiar with the minimum solvency margin calculation formula; – be familiar with the main margin coverage components. READING LIST Teaching material given out during the lectures. In-depth reading will be suggested during the course. TEACHING METHOD Lectures. ASSESSMENT METHOD Oral examination. NOTES Professor Nino Savelli receives students as shown on the Mathematics, Financial Mathematics and Economics Faculty notice board.