Recursive approximating to the finite-time Gerber–Shiu function in Lévy risk models under periodic observation

Abstract

In this paper, we study the finite-time ruin problems in the spectrally negative Lévy risk models. Suppose that the surplus process of an insurance company is observed periodically in a finite-time interval, and ruin is declared as soon as the observed surplus level is negative. A finite-time Gerber–Shiu expected discounted penalty function is studied. After approximating the common density function of the successive increments of the observed surplus process by frame duality projection, we propose a recursive method for computing the finite-time Gerber–Shiu function. Error analysis is made for the proposed algorithm, and numerical examples are also illustrated to show accuracy and efficiency of our method.