On the Ruin Probabilities in a Discrete Time Insurance Risk Process with Capital Injections and Reinsurance

The discrete time insurance risk process with a constant interest force is an interesting stochastic model in risk theory. This paper considers the issue of ruin probabilities of an insurer whose portfolio is exposed to insurance risk arising from a discrete time risk model under the constant initial capital, capital injections and insurer's aggregate claim size. Some expressions are obtained for the ruin probabilities within finite and infinite time. We compute the exact and approximation to the density and cumulative distribution of the time to ruin in the continuous risk model with capital injections for some light and heavy-tailed distributions. Additionally, we illustrate our results and try to minimize the infinite time ruin probability for different values of initial capital and level of capital injection.