Discounted probabilities and ruin theory in the compound binomial model (Q1584519)

A discrete-time model is considered. The aggregate claims are modeled as a compound binomial process. The possible claim amounts are integral multiples of the annual premium. The main goal of the paper is to study the function \(f(x,y;u)\), which is the ``discounted'' probability of ruin, given an initial surplus of \(u\), such that the surplus just before ruin is \(x\), and the deficit \(dt\) ruin is \(y\). Applications include an explicit expression for the expected discounted value of a payment 1 at the time of ruin and formulas for the expected time of ruin.