Probability and Stochastic Processes (PPE)

Área

AC Matemática > UC Mestrados

Activa nos planos curriculares

Actuarial Science > Actuarial Science > 2º Ciclo > Unidades Curriculares Obrigatórias > Probability and Stochastic Processes

Ciências Actuariais > Ciências Actuariais > 2º Ciclo > Unidades Curriculares Obrigatórias > Probability and Stochastic Processes

Nível

2º Ciclo (M)

Tipo

Não Estruturante

Regime

Semestral

Carga Horária

Aula Teórica (T): 0.0 h/semana

Aula TeoricoPrática (TP): 4.5 h/semana

Trabalho Autónomo: 165.5 h/semestre

Créditos ECTS: 8.0

Objectivos

- It is our aim with this Curricular Unit that students acquire the necessary background to precede to the study of other more advanced stochastic phenomena that arise in insurance business, in more advanced Curricular Units.
- The first part of the Curricular Unit is intended to introduce important concepts of probability distributions and their characteristics. In addition to a more advanced study of topics already taught in the first cycle, new concepts are introduced, with actuarial science applications, as is the case of measures for evaluating the tails of the distributions.
- In the second part some of the most relevant stochastic processes used for modelling actuarial phenomena are introduced.

Programa

- Distributions and basic distributional quantities: random variable, distribution and survival functions, multivariate random variables, moments, quantiles, generating functions, sums of random variables, residual life, censored random variables, limited random variables, tails of distributions
- Characteristics of actuarial models: the role of the parameters, the exponential and the linear exponential family
- Continuous models: creating new distributions; identification of some distributions; extreme value distributions
- Introduction to copulas
- General notions of stochastic processes and their classification
- Discrete time Markov chains
- Continuous time homogeneous Markov chains
- Time Inhomogeneous Markov Chains
- Actuarial Applications

Metodologia de avaliação

Sessions are of a theoretical-practical nature, based on oral presentations, accompanied by the projection of slides containing the main results, which will be derived, explained and exemplified.
Students must solve the recommended exercises, as assigned homework, so that proposed solutions may be discussed in the class. The final grade, on the scale of 0 to 20, is assigned on the basis of a written exam.

Bibliografia

Principal