Knowledge and understanding:
The course aims to let acquire knowledge and understanding of the theoretical models and techniques in actuarial statistics. In particular, the first part concerns a priori rate-making and provides the general framework, both methodological and practical, on the use of Generalized Linear Models (GLM) in rate making. Moreover, the first part is devoted to stochastic models in loss reserving, in particular those based on GLM.
The second part deals with mortality models for insurance data and their estimation methods.

Applying knowledge and understanding:
The course aims to let acquire abilities for data analysis in SAS and R, for building models and suggesting solutions to problems connected with the objects of studying, also by highlighting the involved risk levels.

Making judgements: The student must deeply understand the concepts presented during the course, and be able to apply them in different situations.

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 provided in the following courses are necessary: mathematics, probability, statistics and actuarial mathematics.

FIRST PART. STATISTICAL MODELS FOR GENERAL INSURANCE
Non-life insurance pricing.
Generalized Linear Models for insurance rating.
Extreme Value Theory and applications to large claims.
Claims reserving and Generalized Linear Models for the incremental payments.
Recent data analytic models and their application to actuarial issues (introduction).

SECOND PART. STATISTICAL MODELS FOR SURVIVAL ANALYSIS
Survival models in actuarial statistics.
Estimation of survival models.
Generalized Linear Models for survival analysis.
Deterministic and stochastic mortality projection methods.

References

Gigante P., Picech L., Sigalotti L. (2010), La tariffazione nei rami danni con modelli lineari generalizzati, EUT
Wüthrich, M.V., Merz, M. (2008) Stochastic claims reserving methods in insurance. Wiley, Chichester
Wüthrich, M.V., Merz, M. (2015). Stochastic claims reserving manual: advances in dynamic modeling. Swiss Finance Institute Research Paper No. 15-34, SSRN: https://ssrn.com/abstract=2649057
Wüthrich, M.V., Buser, C. (2023). Data analytics for non-life insurance pricing, https://papers.ssrn.com/abstract=2870308
Pitacco E. (2000), Matematica e tecnica attuariale delle assicurazioni sulla durata di vita
London D. (1997), Survival model and their estimation, Third Edition, Actex Publications
Renshaw A. E. (1991), Actuarial graduation practice and generalised linear and non-linear models, Journal of the Institute of Actuaries, 118, II, 295-312
London D. (1985), Graduation: the revision of estimates, Actex Publications
Pitacco E., Denuit M., Haberman S. and Olivieri A. (2009), Modeling Longevity Dynamics for Pensions and Annuity Business, Oxford University Press.


More references will be suggested during the lessons

FIRST PART. STATISTICAL MODELS FOR GENERAL INSURANCE
Generalities on non-life insurance. Preliminary analysis. Defining the levels of tariff variables through cluster-analysis methods. The Ward method. SAS examples.
Generalized Linear Models (GLM) and their application. GLM and quasi-likelihood models. Individual and grouped data. Fitting GLM in SAS. Models for claim numbers. The role of exposures. Poisson, overdispersed-Poisson and negative binomial distributions.
Model for claim amounts. Gamma, inverse-Gaussian, Pareto and lognormal distributions. Jorgensen-de Souza models for the total amount of claims.
Extreme Value Theory and applications to large claims. Mixture models for the claim amounts.
Generalized Linear Models for incremental payments. Analyses of different regression structures and distributions for the response variables. Prediction and prediction error of future payments, reserves and payment cash flow. Connection with some classical claim-reserving methods. SAS examples. Models for the risk margin and for the risk capital in claims reserving.
Recent data analytic models and their application to actuarial issues (introduction).

SECOND PART. STATISTICAL MODELS FOR SURVIVAL ANALYSIS
Survival models in actuarial statistics. Aggregate and select mortality tables. Actuarial survey of mortality. Non-parametric estimation of survival models. Survival multiple decrement model. Non-parametric estimation of survival multiple decrements models. Generalized Linear Models for survival analysis. Parametric estimation of survival multiple decrement models. Cox model. Deterministic and stochastic mortality projection methods.

Lectures supported by slide presentation.

The arguments developed in the course are directly connected with the other actuarial courses, in particular with Matematica attuariale delle assicurazioni danni, Matematica attuariale delle assicurazioni vita, Tecnica attuariale delle assicurazioni danni.

Teaching material is available on the page of the course in Moodle 2.

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 aim to test a sound knowledge and comprehension of the arguments presented during the lessons. The students must prove their comprehension of the fundamental concepts explained in the course and their ability of connecting the different topics; moreover, they must be able to present the acquired knowledges clearly.
In addition, students must present the results of two practical group reports on the first and second part of the module. More details will be provided by the lecturers during the course.

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