Solving the Finite-Time Ruin Problems by Laguerre Series Expansion

In this paper, we study the finite-time ruin problems in the perturbed compound Poisson risk model. The finite-time Gerber-Shiu discounted penalty function and its decomposition are studied. Different from the Laplace transform method, we propose a novel method for computing the finite-time Gerber-Shiu functions by the Laguerre series expansion. When the individual claim size density function is a finite combination of exponentials,we derive the infinite series expansions for the Gerber-Shiu functions. Some numerical examples are also given to confirm the applicability of our method.