The Gerber-Shiu Discounted Penalty Function for Risk Process with Double Markovian Environment
In this paper, we study the Gerber-Shiu discounted penalty function. We shall consider the case where the discount interest process and the occurrence of the claims are driven by two distinguished Markov process, respectively. Moreover, in this model we also consider the influence of a premium rate which varies with the level of free reserves. Using backward differential argument, we derive the integral equation satisfied by the expected discounted penalty function via differential argument when interest process in every state is perturbed by standard Wiener process and Poisson process. In some special cases, closed form expression for these quantities are obtained.
W. G. Yu "The Gerber-Shiu Discounted Penalty Function for Risk Process with Double Markovian Environment", Advanced Materials Research, Vols. 108-111, pp. 1103-1108, 2010