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

In this paper, the classical risk model with exponential claim sizes is considered. The explicit expression of the Gerber-Shiu discounted penalty function psi (x, delta, t) and discounted moments phi(m) (x, delta, t) on finite time horizon is obtained, where delta > 0 is the force of interest, x - the initial reserve. Also the expression of the Gerber-Shiu discounted penalty function on time interval [t(1), t(2)] is derived. The dependance of discounted penalty function on the main parameters x, theta, lambda, delta, mu is presented in diagrams, where lambda > 0 is the parameter of Poisson process, theta > 0 is the safety loading coefficient and mu is the parameter of claim distribution.