Bounds And Approximations To The Ruin Probability Of A Continuous-Time Risk Model

In this paper, we use the idea of the classical risk model and consider a continuous-time risk model with inter-occurrence times following the deficit-time geometric distribution .By an application of the key renewal theorem in the case of the lattice distribution we derive Lundberg bounds , Cramer-Lundberg approximations to the ruin probability and finite-horizon Lundberg inequalities.This paper consists of three chapters.The first one is the preparatory knowledge underlying this paper ,including the basic concepts of the piece-wise deterministic Markov processes(PDMP),the renewal equation ,the key renewal theorem and some results about the classical risk model, which come from [2],[8]and[9].The second one introduces the results about the general ruin probability in a kind of continuous-time risk model with the deficit-time geometric distribution of inter-occurrence times,in which claim sizes are discretly distributed.These come from [6].The main body of this paper is the third one where we derive Lundberg bounds ,Cramer-Lundberg approximations to the ruin probability and finite-horizon Lundberg inequalities .