Ruin Probabilities for the Perturbed Compound Poisson Risk Process with Investment

In this article, we consider the perturbed compound Poisson risk process with investment incomes. The risk reserve process is perturbed by an independent Brownian motion and the surplus is invested at a constant force of interest. We investigate the asymptotic behavior of the ruin probability as the initial reserve goes to infinity. Bounds and time-dependent bounds are derived for the ultimate ruin probability and the probabilities of ruin within finite time, respectively. We also obtain an explicit expression for the Laplace transform of the ultimate ruin probability.