On a discrete-time risk model with general income and time-dependent claims

We consider a discrete-time risk model with general premium rate and time-dependent claim sizes, in which the interclaim time has an impact on the subsequent claim size. By studying the roots of Lundberg's generalized equation, we first obtain an analytical expression for the generating function of the expected discounted penalty function. Then it is shown that the expected discounted penalty function satisfies a defective renewal equation. Moreover, a closed-form expression for the generating function of the time to ruin is obtained when the claim sizes have discrete Km distributions. Numerical examples are also given to illustrate the applicability of the results obtained.