Risk Theory
1
2017-2018
02002275
Mathematics
Portuguese
Face-to-face
SEMESTRIAL
6.0
Elective
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)
NoSyllabus
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
Grading includes work on a (large) numerical problem. This amounts for 25% of the final grading. The remaining 75% are obtained from a final exam. The possibility of getting these 75% by partial exams is offered, possibly accompanied by short problem solving along the semester.: 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.