Two Types Of Bankruptcy Risk Model

Nowadays,risk theory is a hot topic both in actuarial science and mathematics research.The classical risk model,as the foundation of risk theory,is an important stochastic process with properties of temporal homogeneity and independent increment.The study on this model is nearly perfect and exact calculated results for all actuarial diagnostics are derived in analytical form.However,due to limitations of classical risk model,many scholars have been generalized it from various aspects.In recent years,many scholars have studied risk model with individual claims size is Heavy-tailed.This thesis mainly deals with two types of risk models which the individual claims size is the class S(γ).In chapter 1,the author gives a brief introduction of the development of the risk theory,the main results in classical risk model and the generalized direction etc.In chapter 2,the author gives a brief introduction of basic concepts and some mathematical tools are used in this paper.In chapter 3,under the assumption that the claim size is the class S(γ),the author establishes a asymptotic formula for the finite-time ruin probability of the compound Poisson model whose premium is a stochastic process with constant interest force.Then,we generalize it to bidimensional risk model,we also obtain an explicit asymptotic formula for the finite-time ruin probability for the case of Subexponentiality claims.In chapter 4,under the assumption that the claim size is the class S(γ),the author discusses the ruin problem in the risk model perturbed by diffusion.First,we obtain a asymptotic formula for the finite-time ruin probability when the perturbation process is a Brownian motion.Then, we generalize the perturbation process to a quite general stochastic process.Under the assumptions for the unperturbed risk model,we obtain some beautiful results for the finite-time probability in the perturbed risk model.