On the Gerber-shiu Penalty Function for the Compound Binomial Risk Model with Delayed Claims

Abstract: In this paper we consider the Gerber-Shiu penalty function in the compound binomial risk model with time-correlated claims. It is assumed that each main claim will induce a by-claim but the occurrence of the by-claim may be delayed with a certain probability. Formulas for the probability generating function of the penalty function are obtained, together with the expression for the penalty function with zero initial surplus. Then we show that the penalty function satisfies a defective renewal equation. When the claims follow geometric distributions, explicit expression for the Gerber-Shiu function is derived. Numerical example is provided to illustrate the application of the result discussed in the paper.