The Research Of Ruin Probability On Dependent Risk Model

In classic risk model, some scholars usually assume that random variables areindependent, but this is not confirmed with real world. In this thesis, we assume that thereis a dependent structure between some important random variables and apply Copulafunction to describe this structure. Then, we set up dependent risk model and obtain someproperties of ruin probability.This paper can be taken into three parts. In first part, we consider a Sparre Andersenrisk process in which the distribution of the interclaim time is the sum of two independentexponential random variables. We introduce a dependence structure between the claim sizeand the interclaim time. The structure is based on FGM copula. An integro-differentialequation for Gerber-Shiu function is derived and an explicit expression for the Laplacetransform of ruin probability is given for exponential claim size.In second part, we consider that the surplus of an insurer follows compound Poissonprocess and the insurer would invest its surplus in risky assets, whose prices are assumedto satisfy Black-Scholes model. In this risk process, we decompose the ruin probabilityinto the sum of two ruin probabilities: the probability that ruin is caused by a claim, and theprobability that ruin is caused by oscillation. We derive the integro-differential equationsfor these ruin probabilities. When claim sizes are exponential distributed, third-orderdifferential equations of ruin probabilities are derived from the integro-differentialequations and a lower bound is obtained.In ruin theory，we often do not consider the interest rate, or just consider the ruinproblem under the constant interest rate. But in fact, affected by external economic factors,stochastic interest rate are closer to fact. In third part, we focus on the ruin probability ofinsurance company with stochastic interest rate. For the discrete risk model, we usemartingale theory to obtain the final ruin probability of the exponential upper bound.