Research On Ruin Characteristics Of The Discrete Time Risk Model With Delayed Claims

In this paper we mainly study two classes of discrete time risk models with delayed claims.Firstly,we extend the classic discrete time risk model with delayed claims to the case where the premium income process is a binomial process,and we assume that the main claim causes a by-claim with a certain probability rather than probability 1.Secondly,we consider a discrete inter-action risk model with delayed claims with stochastic premium incomes in the case of the discount rate is driven by a time-homogeneous Markov chain with a finite state space.The so-called interaction risk model with delayed claims is that there are two classes of claims,each main claim in one class induces a by-claim in the other class,and the by-claim may occur at the same time as the main claim and may be delayed to the next period.Based on the above two classes of models,using the technique of generating function,we derive an explicit expression or a recursive formula for the Gerber-Shiu discounted penal-ty function.As applications,the joint distributions of the surplus one period prior to ruin,the deficit at ruin,the probabilities of ruin as well as other ruin characteristics are obtained.Finally,some numerical illustrations from some specific examples are also given.