| Abstract [eng] |
In this thesis, the discrete time risk model with inhomogeneous claims is considered. This model is used for describing the insurer‘s capital and its components: initial capital, premiums received, and claims paid. The main risk measures, ruin probabilities and Gerber-Shiu function, are investigated and recursive formulas are obtained. These formulas give fast and accurate evaluation of the finite time ruin probabilities and Gerber-Shiu function. However, the infinite time investigations require that the Gerber-Shiu function's values for the initial capital equal to 0 must be known. This is slightly more difficult due to the claim inhomogeneity and for this reason a theorem with explicit expression of the infinite time Gerber-Shiu function for a zero initial capital is proposed. However, for the calculation of the infinite time values, some assumption about underlying claim structure must be made. As a solution the cyclically distributed claims are proposed, the algorithms for application of the theorems are given and numerical examples with graphical output are presented. Finally, a special case of discrete time risk model with inhomogeneous claims distributed according geometric law is investigated. In addition to the main results, another discrete time risk model with inhomogeneous claims acquiring rational values is investigated. Two theorems for evaluation of the finite time ruin probabilities are proved and some examples are presented. |
