# Risk Theory

**Year**

1

**Academic year**

2022-2023

**Code**

02002275

**Subject Area**

Matemática

**Language of Instruction**

Portuguese

**Other Languages of Instruction**

English

**Mode of Delivery**

Face-to-face

**Duration**

SEMESTRIAL

**ECTS Credits**

6.0

**Type**

Elective

**Level**

2nd Cycle Studies - Mestrado

## Recommended Prerequisites

Basic courses in Differential and Integral Calculus, Probability and Statistics; acquaintance in elementary notions in Stochastic Processes.

## Teaching Methods

Classes are of expository nature and include problem solving. Resolution of numerical problems should support by use of computing methods.

## Learning Outcomes

The main goal is to introduce basic techniques and models in Actuarial Risk Theory., aiming at showing how to numerically the available information.

This course develops mathematical modeling skills and the ability to use them to produce effective answers to real questions. It also aims at developing numerical skills.

## Work Placement(s)

No## Syllabus

Probability Complements: distributions, Riemann-Stieltjes integration, convolution, generating functions, distribution mixing.

Utility Theory: utility functions and the null utility principle.

Individual Risk: estimation, numerical treatment, applications of the Central Limit Theorem.

Collective Risk: compound distributions, classes (a,b,0) and modifications at the origin, recursive algorithms, approximation to the normal distribution.

Ruin Theory: discrete models, Cramer-Lundeberg model, functional equations.

## Head Lecturer(s)

Paulo Eduardo Aragão Aleixo e Neves de Oliveira

## Assessment Methods

Assessment

*Exam: 100.0%*

## Bibliography

S.A. Klugman, H. Panjer, G.E. Willmot, Loss Models, John Wiley & Sons, 2008.

R. Kaas, M. Goovaerts, J. Dhane, M. Denuit, Modern Actuarial Risk Theory, Kluwer Academic Publishers, 2001.

M.L. Centeno, Teoria do Risco na Atividade Seguradora, Celta Editora, 2003.