Knowledge and understanding:
The aim of the course is to present the basic concepts, models and methods in non-life insurance mathematics, in particular those regarding premium calculation, practical aspects of rate making and the estimation of the technical reserves.

Applying knowledge and understanding:
With respect to the topics dealt with, the course aims letting the students to get the ability to apply models and techniques to real cases; in particular, to evaluate, on the base of data, the main technical indexes and the premium in general insurance.

Making judgements: The student must deeply understand the concepts presented during the course, and be able to apply them to situations other than those illustrated.

Communication skills: The student should be able to communicate effectively the concepts learned during the course.

Learning skills: The student should be able to develop learning skills which are essential to the understanding of more advanced issues.

In order to understand the topics dealt with in the course, the concepts of basic mathematics, probability, statistics and financial mathematics are necessary. The following courses are propaedeutic: Calcolo delle probabilità, Matematica finanziaria.

Risk and insurance.
Insurance contracts and random financial transactions.
The premium in non-life insurance.
Description and evaluation of the aggregate claim amount.
Premium evaluation on the base of statistical data/Indexes that summarize the claim experience.
Premium rating.
Basics on reinsurance.
Annual technical result and technical reserves.
Solvency.
Motor third party liability insurance.

References

L. Daboni (1993), Lezioni di tecnica attuariale delle assicurazioni contro i danni, Lint, Trieste
P. Gigante, L. Picech, L. Sigalotti (2010), La tariffazione nei rami danni con modelli lineari generalizzati, EUT (Cap. 1, Cap. 2)
S. A. Klugman, H. H. Panjer, G. E. Willmot (2008), Loss Models: From Data to Decisions, 3th Edition, Wiley
E. Pitacco (2002), "Elementi di matematica delle assicurazioni", Lint, Trieste
A. Olivieri, E. Pitacco (2010), Introduction to Insurance Mathematics. Technical and Financial Features
of Risk Transfers, Springer


More references will be suggested during the lessons.

Risk and insurance: Risk management. Introductory remarks on risk and insurance. A brief description of non-life insurance contracts and products.
Insurance contracts and random financial transactions: Preference orders on random amounts. The expected value criterion. The expected utility criterion. Risk aversion. Some applications in insurance. Safety loading.
The premium in non-life insurance: Premium structure, equivalence premium, pure premium, office premium. Premium principles.
Description and evaluation of the aggregate claim amount: Basic insurance arrangements. Theoretical framework for the evaluation of the aggregate claim amount. Models for the distributions of the number of claims, of the loss amount of a single claim and of the total claim amount for a single contract and for a portfolio. Compound distributions.
Premium evaluation on the base of statistical data/Indexes that summarize the claim experience: Risk premium, claim frequency, average claim severity, premium rate.
Basics on a priori rating: Risk classification. Additive and multiplicative tariff models.
Experience rating: Basics on Bayesian, credibility and bonus-malus approaches.
Basics on reinsurance: Main reasons for reinsurance. Reinsurance arrangements.
Annual technical result and technical reserves: Premium reserve and claims reserve, earned premiums, incurred claim amount. Basics on the balance sheet of a non-life insurance. Indexes/ratios of the portfolio performance.
Solvency: Risk capital.
Motor third party liability insurance: Generalities. Direct reimbursement scheme. Data of the Italian market.

Lectures supported by slide presentations.

Non-attending students are invited to contact the teacher for further suggestions on the course program and bibliographic references.

The examination consists of an oral exam with open questions, that aims to test a sound knowledge and comprehension of the arguments presented during the lessons. The students have to prove their comprehension of the fundamental concepts explained in the course and their ability of connecting the different topics; moreover, they have to be able to present the acquired knowledges clearly.

The course deals with topics strictly connected with one or more goals of the 2030 Agenda for Sustainable Development of the United Nations.