Stochastic calculus in a risk model with stochastic return on investments.

In this paper, we consider a perturbed risk model with stochastic return on investments. After discretizing of the renewal risk process, using the elementary properties of the classical conditional expectation, the Markov property and considerating the ordinary differential equation of a common density function of the inter-arrival times, we introduce a general integro-differential equation for the Laplace transform of the time of ruin with a positive initial surplus. The special cases, for different inter-arrival times distributions, are given in some details in the discrete renewal risk process. [ABSTRACT FROM AUTHOR]