On The Expected Discounted Penalty Function For Some Classes Discrete Time Delayed Renewal Risk Process

In the actuarial literature, it is assumed that a claim occurs at time0inthe ordinary discrete time renewal risk process. However, this assumption maybe restrictive in insurance reality. The delayed renewal risk model can solve thisproblem, in which the distribution of the first claim occurrence time is assumedto be independent of subsequent claim times, but can have different distributions.In the present thesis, we aim to investigate the expected discounted penaltyfunction for some classes discrete time delayed renewal risk models.Chapter1summarizes related studies for classical discrete time riskmodels, including compound binomial model, discrete time renewal risk modelswith K_m inter-claim times and general inter-claim time, and so on. In chapter2the expected discounted penalty function for two classesdelayed renewal processes are studied. Section1introduces the structure of therisk models. In section2, we express the penalty function in the ordinaryrenewal model. Section3gives the explicit for the tail of deficit in the stationaryrenewal risk process.In chapter3, we study the penalty function with geometrical claimamounts. Section2derives the expressions for φ_v,1^d（u）, in which only deficitdistribution is involved. When the penalty function depends on the surplus priorto ruin and the deficit at ruin, the expression for φ_v,s^d（u） is obtained in section3.