| Abstract [eng] |
The topic of the thesis is the calculation of risk measures in inhomogeneous discrete time risk models with independent and dependent claims. Firstly, the algorithm for calculating the values of the particular case of the Gerber-Shiu discounted penalty function in bi-seasonal discrete time risk model was derived. Also, the algorithm for computing the values of the ultimate ruin probability in bi-seasonal discrete time risk model with dependent claims was created. In this model, the case when net profit condition is not satisfied was investigated as well. In the practical part of the thesis, the applicability and computational properties of the algorithms were investigated with numerical examples. Furthermore, methods were created for measuring approximation errors of the algorithms. The results of the thesis extend the results obtained by Damarackas and Šiaulys (2014). In their paper the calculation of ruin probability in the bi-seasonal discrete time risk model was considered. Both more general risk measure (Gerber-Shiu function) and more general model are considered in the thesis. Bi-seasonal model with dependent claims is introduced for the first time in the thesis. Furthermore, with dependent and differently distributed claims, recursive calculation of ruin probability in any kind of discrete time risk model was not considered in the scientific literature before. Besides that, was derived the new algorithm for calculating Gerber-Shiu function values which is both more computationally feasible and less prone to numerical errors than the existing solutions found in the literature. The main results of the thesis were proved using the classical methods of probability theory and mathematical analysis, with an emphasis on discrete differentiation. |
