17274 - Actuarial Techniques

Learning outcomes

At the end of the course students know the methods to compute premiums (fair, pure, gros) in both life and non-life insurance policies. Students will also learn how to compute reserves and profits in both life and non-life insurance.

Course contents

Life insurance: very brief survey of probability models for life and of financial mathematics; standard contracts: endowment, life insurance, annuity. Commutators. Fair premium, loadings, gros premium. Reserves (retrospective and prospective). Fouret equation, Kanner equation. Reserving with expenses. Technical basis (first and second order), methods to select a first order basis. Profit, Homans' decomposition, profit signature. With-profits policies, basic tools for pricing equity-linked policies.     

Non life insurance: main types of contracts, fair premium, loadings, gros premium, indifference premium, premium principles. Main probability models for the distribution of the number of claims and of the claim severity. Mean and variance of a portfolios of homogeneous risks, moment generating function. Claim frequency, index of repeatability. Auto insurance policies, prior and posterior premium. Premium and claim reserves. Chain-ladder method (with and without inflation adjustment), an overview of Fisher-Lange.

 

Readings/Bibliography

Pitacco E.: Matematica e Tecnica Attuariale delle assicurazioni sulla durata di vita, Lint, Trieste, 2000.

Pitacco E., Olivieri A.: La valutazione nelle assicurazioni vita, Egea, Milano, 2005.

Olivieri A., Pitacco E.: Introduction to Insurance Mathematics - Technical and Financial Features of Risk Transfers, Springer, 2011.

Spelta D.: Teoria matematica delle assicurazioni sulla vita, Pitagora, 2001.

Daboni L.: Lezioni di tecnica attuariale delle assicurazioni contro i danni, LINT, Trieste, 1993.

Cerè M., Spelta D.: Esercizi di matematica attuariale, Esculapio, 2017.

Teaching methods

Theoretical explanations will be alternated with practical examples and test-cases. Some problems given in the past exams for becoming Italian actuaries will also be solved.

Finally, the course will be preceded by a crash-course (in which the basic facts about demography/financial mathematics will be recalled). Students are strongly encouraged to attend it.

Assessment methods

The learning outcomes are verified through a written exam, which

takes two hours. Students must demonstrate both theoretical and practical skills. Therefore, the exam consists of both practical problems (two or three) and one free-response question. The use of books is not permitted. Pocket calculators are allowed.

Teaching tools

The lessons will be mainly tought via slide projection (the slides will be made available on the teacher's website, so that students can download them). Students are encouraged to download the slides before going to lesson, such to better follow the teacher's explanation. The core concepts and formulas will also be presented using the blackboard.   

Office hours

See the website of Luca Vincenzo Ballestra