# Non-Life Insurance Pricing

## Objectives

Learn the basic techniques for Pricing in Non-life Insurance.

Distinguish A Priori Ratemaking from A Posteriori Ratemaking.

Distinguish Premium Calculation from Tariff Construction.

Know how to build a Tariff Structure for Non-life Insurance using Generalized Linear Models and Credibility Theory.

Know how to implement a Bonus-Malus System and evaluate its effectiveness.

## General characterization

12457

6.0

##### Responsible teacher

Gracinda Rita Diogo Guerreiro

Weekly - 4

Total - 70

Inglês

No requirements

### Bibliography

Buhlmann, H. and Gisler, A. (2005). A Course in Credibility Theory and its Applications, Springer.

Charpentier, A. (2015) Computational Actuarial Science with R, Chapman and Hall/CRC Press

Dobson, A. (1990), An Introduction to Generalized Linear Models, Chapman & all, London.

Lemaire, J. (1995), Bonus-Malus Systems in Automobile Insurance, Kluwer Academic Publishers.

Ohlsson, E.; Johansson, B. (2010), Non-Life Insurance Pricing with Generalized Linear Models, Springer.

### Teaching method

In lectures we will explain and discuss program topics of the course.

The themes are introduced by the teacher, consolidated with real examples taken from the general insurance industry following a brief discussion.

The lectures include the resolution of real life examples in a computational environment.

The evaluation will be performed with tests, practical assignments and/or final exam.

### Evaluation method

Evaluation Rules

Frequency

To obtain Frequency to the UC the student must perform a Presentation of one of the Practical Assignments of the CU..

CONTINUOUS EVALUATION / NORMAL SEASON

The continuous assessment will be made through two mini-tests (MT1 and MT2), two practical group assignments (TP1 and TP2) and one oral Presentation (P)

Grade Normal Season = 0.20 (MT1+MT2) + 0.25 (TP1+TP2) + 0.10 P , with (MT1+MT2+A)/3 >= 7

The student who obtains a final grade greater than or equal to 18.5 must take an oral defence of grade (on a date to be agreed). If the student does not attend the oral exam, the final grade will be 18 points.

The student obtains approval to UC if Grade Normal Season is greater than or equal to 9.5 values.

EVALUATION OF APPEAL SEASON

The evaluation of Appeal Season is made by Exam (E), being valid both for grade improvement and for approval to UC.

Grade Appeal Season = 0.5 E + 0.25 (TP1 + TP2) , with E >= 7

The student obtains approval to the CU if the Grade of Appeal Season is greater than or equal to 9.5 values.

The student who obtains a final grade greater than or equal to 18.5 must take an oral defence of grade (on a date to be agreed). If the student does not attend the oral exam, the final grade will be 18 points.

Students who intend to take the appeal exam, with a view to improving their grades, must, in advance, request this improvement from academic services.

Practical assignments cannot be improved.

## Subject matter

1. A priori Ratemaking

1.1 Credibility Theory

Bayesian credibility: Introduction and Poisson-Gamma Model

Buhlmann and Bulhmann-Straub Models

Jewel’s Hierarchical Models

1.2 Generalized Linear Models in Non-life Insurance Pricing

The Exponential Family

Model formulation

Model Selection and Parameters estimation

Modeling Claim Frequency

Modeling Claim Severity

Building the Pricing Structure

Inclusion of Large Claims

Logistic Regression in Pricing Context

2. A Posteriori Ratemaking

A priori vs a posteriori ratemaking

Bonus Malus Systems definition

Transition Probabilities and Limit Theorems