# Insurance mathematics (2015/2016)

Course code
4S003194
Name of lecturers
Paolo Frigo, Massimo Franchetti
Coordinator
Paolo Frigo
Number of ECTS credits allocated
6
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Language of instruction
Italian
Period
Secondo Semestre Magistrali dal Feb 22, 2016 al Jun 1, 2016.

#### Learning outcomes

The course will provide students with the mathematical and logical skills needed to address the main actuarial problems in life and non-life insurance, with particular reference to the determination of premiums and reserves as well as the evaluation of profitability and riskiness of insurance portfolios.
The course consists of two modules, dedicated to Life and non-Life insurance. During the semester some seminars on selected topics, held by industry experts, will be offered.

#### Syllabus

Non-Life Module
1. Basic knowledge
• Basics of insurance business: risk transfer, risk pooling, types of non-life insurance, technical management of portfolios
• Premium calculation through statistical observation
2. Risk theory
• Introduction to collective risk theory: the compound model
• Claims count and severity distributions
• Parameters estimation
• Methods for calculating the compound distribution (hints)
3. Tariffication
• Risk classes
• Simple tariffication methods
4. Claims reserving
• Introduction and triangular representation of data and indicators
• Deterministic algorithms: Chain Ladder, Bornhuetter-Ferguson, Fisher-Lange (hints)

Life Module
1. Basic Knowledge
• Mutuality and Solidarity
• Life insurance products
• Life table
2. Premiums and Reserves
• Technical rate (difference between prudential basis and realistic basis)
• Actuarial values
• Mathematical reserve
• Surrender values and paid-up values
3. Finance in life insurance
• With-profit policies
4. Profits in a life insurance portfolio
• The total profit
• Mortality/Longevity Risk
• Profit Testing

Topics of the seminars:
• Reinsurance
• Pension plans
• Solvency II

Textbooks
Non Life Module:
• Wuthrich, Mario V., Non-Life Insurance: Mathematics & Statistics;
free download in SSRN newtowk at http://ssrn.com/abstract=2319328 or at http://dx.doi.org/10.2139/ssrn.2319328
Life Module:
• Olivieri Annamaria, Pitacco Ermanno: Introduction to Insurance Mathematics – Technical and Financial Features of Risk Transfers, Springer (2011);
http://www.springer.com/mathematics/applications/book/978-3-642-16028-8

#### Assessment methods and criteria

A spoken test will be held. The test has the purpose to verify breadth and depth of the acquired knowledge, models learnt, property of language.