The Applications Of Thinning Process In Two Kinds Of Multiple-Type Risk Model With Dependent Claims Number Process

In insurance mathematics, ruin theory is the mainly content of insurance risk theory, as can supply a very useful early-warning measure for the risk of the insurance company, it has important theoretical and practical significance for the insurance company. In this dissertation, we extends the classical risk model, and mainly discuss the ruin probability of two kinds of multiple-type risk model with dependent claims number process.In auto insurance, while an accident happens, some other kinds of claims are always caused, such as persons' injury insurance and property insurance. Then we discuss this kind of dependent risk model in two aspects:1,We suppose every auto accident can cause each kinds of damage claim with a fixed probability. And we suppose it only cause persons' injury claim with probability p,it only cause property damage claim with probability q,it cause not only persons' injuryb ut also property damage claim with probability l, and it doesn't cause any kind of claim with probability s.And 0≤p,q,l,s≤1, p+q+l+s=1. When an accident happens, it certainly cause auto claim. We suppose auto claim number process is a homogeneous Poisson process with parameterλ. Then we get a multiple-type risk model with dependent claims number process. In this section, we change the dependent risk model into independent risk model by using the decomposition of homogeneous Poisson process. Then get the ruin probability and an estimation of its upper bound by using the martingale theory which is usually used in insurance risk theory.2,We discuss the ruin probability under the circumstance that every auto accident cause other kinds of claims with a unfixed probability which is the function of time t.We suppose that it cause other claims with p(s), q(s), l(s), v(s) respectively. Similarly, we change the dependent risk model into independent risk model by using the decomposition of homogeneous Poisson process and get the upper bounds of the ruin probability.The method of simplifing the dependent risk model used in this dissertation has a good effect on the operation of the insurance company. It can also be used in the same risk model, so the method has a practical significance.