Download Actuarial Mathematics (module II)

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.