79044 - Statistical Models for Actuarial Sciences

Learning outcomes

The student will be able to specify and estimate statistical models for different kind of data. That is, binary, counting and ratio data. The student will be able to choose the most appropriate statistical model for a specific problem, estimate the paramters and make inference. He/she will be able to use statistical software desigend for actuarial models.

Course contents

• Introduction. Review of calculus and linear algebra. Non-life insurance pricing. Claim frequency and claim severity. Multiplicative and addittive models.
• The Generalized Linear Model. Linear regression model review. The exponential family. The Link function. The generalized linear model.
• Estimation of the Generalized linear model. Maximum likelihood. Asymptotic inference: score statistics, wald statistics, likelihood ratio and deviance.
• Hypothesis Testing, model and variable selection. Interactions.
• Models for claim frequencies. Poisson and negative-binomial regressions. Examples.
• Models for claim severity. Gamma or Inverse Gaussian GLMs. Examples.
• Models for the total claim. Compound poisson models. Some Tweedie models. Examples and applications.

Readings/Bibliography

• E. Ohlsson and B. Johansson. Non-life Insurance Pricing with Generalized Linear Models. Springer, EEA Series Textbook. 2010.
• Arthur Charpentier, Computational Actuarial Science with R, CRC Press, 2015 (ebook avalable)
  

Suggested readings:

• J. Dobson, Introduction to Generalized Linear Models. Chapman and Hall/CRC Press. 2001. H. Buhlmann and Alois Gisler, A Course in Credibility Theory and its Applications, Springer Universitext, 2005.

Teaching methods

Blackboard lessons.

Examples and case studies on real car-accidents datasets using R. Tutorials on data analysis and model testing and validation.

Assessment methods

The student will be verified in two pahses.

1. A report on a case study is written and presented. Usually the project is developed by a group of at most 3 people. Exceptionally it can be done by a single person. However, it needs to be presented in full by each student. The evaluation is obtained on the quality of the presentation. The project aim and the aspects  to be studied are assigned during the teaching lessons.

2. Written exam containing exercises and questions on the program.

The student should fix an appointment to present the case study report. The dates of the written exam are fixed and the candidate should register on the almaesami website before the deadlines.

 

Teaching tools

Case-studies in PC-Lab using R, R-Studio and dataset coming from the CASdatasets package.

Office hours

See the website of Paolo Foschi