The finite-time ruin probability under the compound binomial risk model

Abstract

We study the compound binomial ruin model, which is considered to be the discrete analogue of the classical compound Poisson model. Our key result is a simple approach for inverting a generating function whose argument is the discount factor when we know the inverse of the same generating function, which this time has argument that is the solution to Lundberg’s equation. The main idea comes from a result in Dickson and Willmot (ASTIN Bulletin 35:45–60, 2005) who discuss the classical model. We are then able to derive the probability distribution of the time to ruin and to go beyond the results in Dickson and Willmot (ASTIN Bulletin 35:45–60, 2005) by deducing the distribution of the first hitting time of a specific level and the duration of the time when the surplus is negative. The paper contains several illustrative examples where specific claim-amount distributions are considered.