Actuarial Statistics of Stochastic Processes
Presentation of important and fundamental concepts in the statistics of stochastic processes with applications in the actuarial area.
Pedro José dos Santos Palhinhas Mota
Weekly - Available soon
Total - 20
Intermediate level notions of Probability and Statistics, Measure Theory and Stochastic Processes.
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.
Lecture-lab classes, where together with the explanation of the main concepts, illustrative examples are given.
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.
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.