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

In this paper, we study the finite-time ruin problems in the spectrally negative Levy 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. (C) 2021 Elsevier B.V. All rights reserved.