On the evaluation of ruin probabilities in a generalized dual binomial risk model using Markov property

This article is concerned with a reasonably generalized dual Binomial risk model where the periodic premium is one and in each period there is at most one claim and non-negative claim amounts are independent and identically distributed random variables. Our main purpose is to evaluate the probability of time to ruin and ruin probabilities. First, we present a formula for probability of time to ruin based on the convolution of claim amount. We derive a recursive expression for the finite time ruin probability based on the probability of time to ruin and classical ruin probability using the Markov property and law of total probability when surplus process stays below or at zero at least for some fixed duration of time. Moreover, we obtain an explicit expression for the corresponding infinite time ruin probability as a limiting case. Finally, to illustrate our method we calculate the numerical values of these probabilities for some different types of models of probability mass functions for claim amounts.