Insurance mathematics (2020/2021)

Course code
Name of lecturers
Mauro Cortese, Alessandro Ricotta
Mauro Cortese
Number of ECTS credits allocated
Academic sector
Language of instruction
primo semestre (lauree magistrali) dal Oct 5, 2020 al Dec 23, 2020.

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.


Dual teaching (in presence and remotely)

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

Non Life Module
1. Basic knowledge
• Basics of insurance business: risk transfer, risk pooling
2. Introduction to non-life insurance
• Non-life insurance coverages and local branches
• Damage and compensation
• Non-life technical indicators
3. Probability and statistics
• Random variables and characteristic functions, moments and central moments, measures of dispersion and shape.
• Truncated and censored random variables
• Probability distributions: Binomial, Negative Binomial, Poisson, Normal, LogNormal, Gamma, Pareto
4. Premium estimation
• Commercial premium
• Empirical and theoretical approaches to estimate pure premium
• Risk and expenses loadings
5. Collective risk theory
• Risk reserve equation, premium and reserve risk, random variable “total amount of claims”
• Compound Poisson process
• Compound mixed Poisson process
6. MVLI Tariffication
• Average commercial premium estimation
• A priori personalization of premium
7. Technical provisions
• Premium and claims provisions
• Deterministic methods to estimate claims reserve
• Stochastic methods to estimate claims reserve

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.

The written essay is taken in a teaching room or (under a student's request) remotely