Insurance mathematics (2018/2019)

Course code
Name of lecturers
Paolo Frigo, Massimo Franchetti
Paolo Frigo
Number of ECTS credits allocated
Academic sector
Language of instruction
primo semestre lauree magistrali dal Oct 1, 2018 al Dec 21, 2018.

Lesson timetable

Go to lesson schedule

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.


Non-Life Module
1. Basic knowledge
• Basics of insurance business: risk transfer, risk pooling, types of non-life insurance, technical management of portfolios
• Equivalence premium, risk loading calculation principles, net premium
• Premium calculation through statistical observation
• Gross premium
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
• Basic concepts 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
• Net premium, Gross premium
• Technical rate (difference between prudential basis and realistic basis)
• Actuarial values
• Mathematical reserve
• Single premiums, periodic premiums
• Risk premiums and saving premiums
• 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
• ALM (Asset and Liability Management)
• Solvency II

Non Life Module:
• Wuthrich, Mario V., Non-Life Insurance: Mathematics & Statistics;
free download in SSRN newtowk at or at
Life Module:
• Olivieri Annamaria, Pitacco Ermanno: Introduction to Insurance Mathematics – Technical and Financial Features of Risk Transfers, Springer (2011);

Assessment methods and criteria

The exam consists of a two-hour written test, equally divided between the Non-Life and Life modules.
The structure of the test is as follows:
- two numerical exercises, applying models learnt in the course
- some multiple choice questions and some open questions, aimed at verifying the ownership of language and the ability to systematically link the knowledge gained
During the test the use of the calculator will be allowed, but not of personal notes or other teaching material.

Student opinions - 2017/2018