17274 - Actuarial Techniques

Learning outcomes

At the end of the course students know the methods to compute premiums (pure and gros) for life insurance policies. Students will also learn how to compute reserves and analyze their dynamics.

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). Profit, Homans' decomposition.

Non life insurance: basic concepts, mean and variance of a portfolios of homogeneous risks, premium calculation. Claim frequency, average claim cost, repetibility index.

Readings/Bibliography

Students are encouraged to use the teaching material available on the website, which is necessary 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.

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.

SSince they are suggested textbooks, any Edition is fine. 

Teaching methods

The course is structured in frontal lessons in which the main elements of Actuarial Science will be presented, with a main focus on 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.

Assessment methods

The learning outcomes are verified through a written exam, which

takes approximately one hour and twenty minutes. Students must demonstrate both theoretical and practical skills. Therefore, the exam consists of two practical problems and a free-response question. The first exercise, which is in life insurance, will grant up to 15 points (if it is done completely and correctly), the second exercise, which is in non-life insurance, will grant up to 10 points (if done completely and correctly) and the free-response question, which is on the whole program, will grant up to 6 points (if answered correctly). Students who score 31 will be valued "30 e lode". 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 valuing the exam, the teacher will pay attention to the correctness of the procedures used in the exercises and the correctness of the answer to the free-response question. There are no intermediate (inter-course) exams.

Teaching tools

The lessons will be mainly tought via slide projection (the slides are available on the "Virtuale" website (to which students are suggested to sign, checking that the course selected is the one of the three-year laurea degree). 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 45 lesson hours, some meetings will be scheduled with a tutor

Office hours

See the website of Luca Vincenzo Ballestra