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  5. Actuarial Statistics of Stochastic Processes

Actuarial Statistics of Stochastic Processes

Objectives

Presentation of important and fundamental concepts in the statistics of stochastic processes with applications in the actuarial area.

General characterization

Code

9915

Credits

6.0

Responsible teacher

Pedro José dos Santos Palhinhas Mota

Hours

Weekly - Available soon

Total - 20

Teaching language

Português

Prerequisites

Intermediate level notions of Probability and Statistics, Measure Theory and Stochastic Processes.

Bibliography

1 – Lipster, R. S. & Shiryaev A. N. (2001) Statistics of Random Processes second edition, volume I and II, Springer.

2 – Heyde, C. C. (1997)  Quasi-Likelihood and its Application Springer.

3 – Küchler, U. & Sørensen, M. (1997) Exponential Families of Stochastic ProcesssSpringer.

4 – Prakasa Rao, B. L. S.  (1999)  Statistical Inference for Diffusion Type ProcessesArnold, Hodder Headline Group.

5 – Rolski, T. & Schmidli, H. & Schmidt, V. & Teugels, J. (1999) Stochastic Processes for Insurance and Finance John Willey & Sons.

6 – Mexia, J. T. (1996) Introdução à Teoria Estatística do Risco, SPM & CIM.

Teaching method

Lecture-lab classes, where together with the explanation of the main concepts,  illustrative examples are given.

Evaluation method

The evaluation of the course is made ​​from one of two ways:

1)      realization of practical problems with a writing report.

2)      realization of written tests.

Subject matter

1. Statistical theory of risk: The counting process; The compound Poisson process;Probability of ruin.

2. Statistics of Markov chains.

3. Statistics of second order stationary processes.

4. Statistics of Diffusions: Parametric and non-parametric Inference for diffusions.

5. Quasi-likelihood: martingale estimating functions; simulated estimating functions.

6. Statistics of stochastic extremal processes.