# 17274 - Actuarial Techniques

• Campus: Rimini
• Corso: Second cycle degree programme (LM) in Statistical, Financial and Actuarial Sciences (cod. 8877)
• from Sep 18, 2024 to Dec 06, 2024

## 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.

It is expected that the first "inter-course" partial exam will be on the course contents from the beginning up to "Reserving with expenses" included.

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.

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.

Since 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, 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 one hour and thirty minutes. Students must demonstrate both theoretical and practical skills. Therefore, the exam consists of both practical problems (three problems) 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, paying attention to the correctness of the answers and the employed procedures. Each exercise and the free-response question will grant from 6 to 9 points (depending on their level of difficulty), for a Total of 31 points (corresponding to the "30 e lode" grade).

## Teaching tools

The lessons will be mainly taught via slide projection, together with the teacher's explanation (the slides are available on the "Virtuale" website, to which students are encouraged to sign paying attention that the selected course is that of the Master's 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.

## Office hours

See the website of Luca Vincenzo Ballestra

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.