Two Types Of Dependent Risk Model Of Bankruptcy

The risk model with interclaim-dependent claim size has been extensively studied.We discuss the ruin problems of compound Poisson risk model in which the dependencestructure between the claim size and interclaim arrivals. We firstly study the survivalprobability function of the compound Poisson risk model in which has the dependencestructure same as Albrecher(2004). Then we derive some results of compound Poissonrisk model based on Copula dependency.According to the content of this thesis, it’s divided into the following three chapters.In Chapter1, we introduce the background of the problems and also introduce therisk models mainly involved in this thesis:In Chapter2, we introduce the dependency which is similar to Albrecher and Boxma(2004): the quantities {Bi, i=1,2,} are assumed to be i.i.d. random variables. Ifthe i-th claim Xiis larger than a threshold Bi, then the time until the next claim isexponentially distributed with rate λ1>0, other it is exponentially distributed with rateλ2>0.(2) The compound Possion risk model based on Copula dependencyWe assume that the dependence structure for the claim size and interclaim arrivals(Xi, Ti) is based on the CopulaIn Chapter2, we obtain the integro-diferential equation and the Laplace transform of the survival probability function of compound Poisson risk model with Albrecher(2004)dependency.In Chapter3, we study the compound Poisson risk model based on Copula depen-dency, it’s divided into the following four sections. In Section1, we discuss a generalizedLundberg equation. In Section2, we derive the Laplace transform of the Gerber-Shiuexpected discounted penalty function. In Section3, we derive a defective renewal equa-tion for the Gerber-Shiu expected discounted penalty function Φδ(u) by divided diferencewhich is as follows:Finally, we give a defective renewal equation respresentation for the Laplace trans-form of the time to ruin.