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).

 

Readings/Bibliography

Students are encouraged to use the teaching material available on the website, which is essential and sufficient for the exam. Students interested in having a more in-depth knowledge of the subject can look at the following textbooks:

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

The course is structured in frontal lessons in which the main elements of Actuarial Science will be presented, focusing on both life and non-life insurance. 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, as well as a formulary (that must only contain formulas, with no proofs or solved exercises). The exam aims at assessing the students' ability in solving problems in the core fields of the course. In each exam, students will encounter exercises with an increasing level of complexity, so as to test their skills in facing both simple and complex problems.

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. Finally, besides the 60 lesson hours, some meetings will be scheduled with a tutor who will focus on the more practical aspects of the course and will explain to students how to solve various kinds of problems.

Office hours

See the website of Luca Vincenzo Ballestra