Sparse Model Of The Three Characteristics Of The Joint Distribution Of The Discounted Penalty Function

Evolved from the classical risk model, people generalize it in many aspects. For instance, generalize the counting process from poisson process into renewal process and general markov process. Besides,Gerber generalize the classical risk model into model with perturbed diffusion etc. this dissertation, based on papers [3] [4] [23], consider several important acturial concepts of thinning process.In chapter 1: Look back upon the recent result about thinning process and cite some necessary basic knowledge.In chapter 2: Based on the paper [1], at first, we manage to generalize the joint distribution into ruin time, ruin deficit, the maximum surplus of before ruin, and the maximum surplus of before the last time ruin and get the explicit expression when the claim is exponential distribution.In chapter 3: We consider the dismiss the contact and the times of claims are q-thinning, p-thinning process respectively. In this modle, by simulating the classical risk model, based on the paper [3] [4] [23], we obtain the martingale and the upper bound.In chapter 4: Consider the joint distribution of p-thinning process, which the times of claims is p-thinning process of premium, and by dual argument, we obtain the density function of u(t) the first arrival at x before ruin and joint distribution of ruin time, surplus before ruin and the Expression that the deficit at ruin should satisfy.In chapter 5: We discuss the expected discounted penalty function of thinning model. The claims' distributes are using the similar Gerber and Shiu(1998) method. We get a formula of expected discounted function and draw a explicit expression when u=0.