| Abstract [eng] |
In this paper we consider Gerber-Shiu discounted penalty function in the classical risk model for Pareto claims. Our main goal is to construct an algorithm for obtaining values of the discounted penalty function (considering penalty function w=1). Due to the complicated form of the transformed Pareto distribution function we cannot obtain its convolutions analiticaly. We use numerical methods provided by Maple (cube spline) to find interpolating functions instead. Continuously applying recursive formulas we obtain first 5 interpolated convolutions. Then we calculate values of Gerber-Shiu discounted penalty function for certain arbitrary parameters: α – degree of Pareto distribution function, initial surplus u, security loading θ, discounting parameter δ and Poison process parameter λ. We present data tables and graphs of the discounted penalty function for some variations of parameters in later sections. Finally we state that the method that we use is quite complicated. For better accuracy of the discounted penalty function values one may require to get many convolutions of the transformed Pareto distribution function and that may require too great of the resources. However the quantity of the convolutions needed rapidly decreases for large values of the initial surplus u. |
