On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments

Abstract:

      This paper considers the expected discounted penalty function $\Phi(u)$ for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for $\Phi'(0)$ is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.