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CA  >  Actuarial Science  >  Currículo  >  Probability and Stochastic Processes

Master in Actuarial Science

Plano Curricular Actuarial Science


Probability and Stochastic Processes (PPE)

UC Competência

Probability and Stochastic Processes(Matemática)

UC Execução

Probability and Stochastic Processes (2020/2021 - Semestre 1)
Probability and Stochastic Processes (2019/2020 - Semestre 1)
Probability and Stochastic Processes (2018/2019 - Semestre 1)
Probabilidade e Processos Estocásticos (2017/2018 - Semestre 1)
Probabilidade e Processos Estocásticos (2016/2017 - Semestre 1)
Probabilidade e Processos Estocásticos (2015/2016 - Semestre 1)
Probabilidade e Processos Estocásticos (2014/2015 - Semestre 1)
Probabilidade e Processos Estocásticos (2013/2014 - Semestre 1)
Probabilidade e Processos Estocásticos (2012/2013 - Semestre 1)
Probabilidade e Processos Estocásticos (2011/2012 - Semestre 1)

Contextos

Grupo: Actuarial Science > 2º Ciclo > Unidades Curriculares Obrigatórias

Período: 1 Ano, 1 Semestre

Peso

8.0 (para cálculo da média)

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

Loss Models, From Data to Decisions

Klugman, S.A.; Panjer, H.H. & Willmot, G.E.

2008

(3rd edition), John Wiley & Sons, Hoboken NJ.

Stochastic Processes

Ross. S. M.,

1996

2nd ed. John Wiley & Sons, New York.

CT4 Models

Core Reading 2011

2011

The Actuarial Profession

Actuarial Mathematics for Life Contigent Risks

Dickson, D., Hardy, M., and Waters, H.

2009

Cambridge University Press

Introduction to Probability Models

Ross, S. M.

2010

(10th edition), Academic Press, New York

Secundária

An Introduction to Stochastic Modeling

Taylor, H. M. and Karlin, S.

1998

(3rd edition), Academic Press, New York

Teoria do Risco na Actividade Seguradora

Centeno, M.L.

2003

Celta Editora, Oeiras, Portugal.