The Markov Risk Model under Stochastic Discount Interest Force
We investigate the expected discounted penalty function in which the discount interest process is driven by markov process. We obtain the integro-differential equation satisfied by the expected discounted penalty function when interest process is perturbed by standard Wiener process and Poisson-Geometric process. A system of Laplace transforms of the expected discounted penalty function, given the initial environment state, is established from a system of integro-differential equations. One example is given with claim sizes that have exponential distributions.
Y. J. Huang and C. M. Zhang, "The Markov Risk Model under Stochastic Discount Interest Force", Advanced Materials Research, Vols. 179-180, pp. 1080-1085, 2011