INVESTIGATION OF THE GERBER-SHIU DISCOUNTED PENALTY FUNCTION ON FINITE TIME HORIZON

Abstract

In this paper, the classical risk model with exponential claim sizes is considered. The explicit expression of the Gerber-Shiu discounted penalty function (x; ; t) and discounted moments m(x; ; t) on finite time horizon is obtained, where > 0 is the force of interest, x - the initial reserve. Also the expression of the Gerber-Shiu discounted penalty function on time interval [t1; t2] is derived. The dependance of discounted penalty function on the main parameters x; ; ; ; is presented in diagrams, where > 0 is the parameter of Poisson process, > 0 is the safety loading coefficient and is the parameter of claim distribution.