A Class Of Mixed Dividend Policy Dependent Risk Model

In the classical compound Poisson risk model, the claim amounts and the interclaim times are always assumed to be indepenent. In fact, this hypothes is inadequate to depict the realistic circumstances, so more and more risk models with intercaim-dependent claim sizes have been studied. This paper considered the compound Poisson risk model with a hybrid dividend strategy in the presence of interclaim arrivals and claim sizes are de-pendent. In this paper, we get an integro-differential equation for Gerber-Shiu expected discounted penalty function in the risk model and the solution to the equation. Then we analyze the expected discounted dividend payment before ruin in the same risk model. An integro-differential equation is derived and then solved. Finally, the paper give the ruin probability in the special case.The thesis is divided into four chapters based on the contents:Chapter1is preface. Firstly we introduced the risk model with a hybrid dividend strategy in the presence of interclaim arrivals and claim sizes are dependent; Secondly gave the density function of the dependence structure; Finally proposed the compound Poisson risk model with correlation between interclaim arrivals and claim sizes in the presence of a hybrid dividend barrier: where b1,b2(0<b1<b2<∞) are two constant, Ub1,b2(t)is the surplus at time t; u is the initial surplus level,0(?)u<b1<b2are two constant dividend barriers.In Chapter2, we got the nonhomogeneous integro-differential equation satisfied by the Gerber-Shiu expected discounted penalty function under this risk model: when0(?)u(?)b1 when b1<u≤b2where And got the expression of the solution to the equation.In Chapter3, we gave the homogeneous integro-differential equation satisfied by the expected discounted dividend payment before ruin and solve the equation for the same model: when0≤u≤b1when b1≤u≤b2whereIn Chapter4, we gave the ruin probability under some specific circumstances.