Asymptotic Estimate For The Ruin Probability With Heavy-Tailed Claims And Random Economic Environment

The main result of this paper is divided into two parts:firstly, considering the risk threshold under the basis of the continuous-time risk model with investment income. And double investment strategies risk model is established with the aid of Ito stochastic process theory and risk neutral assumptions. Then the asymptotic estimations of ruin probability in finite-time and infinite-time are obtained by assuming the claims process belongs to D, and are pair-wise quasi-asymptotically independent, and the corresponding numerical simulation has carried on; Secondly, multi-risk perturbed model is discussed under single strategy and double investment strategy. And the asymptotic estimations of ruin probability in finite-time and infinite-time are obtained, and the corresponding numerical simulation has carried on.Specially, the paper is organized as follows:The first chapter introduces the development history of ruin theory. Research on the risk model in the basic direction is summarized; And a brief introduction about the current situation of the development of the insurance industry has be made. The foundation of optimizing investment strategy and improving the return on investment is described in view of reality.The second chapter is preliminaries. First, several types of commonly used heavy-tailed distributions and the affiliation between them, as well as the definition of Matuszewska index, quasi-asymptotic independence and part of asymptotic relations have be introduced; and the definition of Ito stochastic processes, as well as Ito formula are given.The third chapter has made the assumption that insurance companies take different investment strategies of different surplus levels. The asymptotic estimation problem of ruin probability in dual investment strategy is discussed from the perspective of optimizing investment strategies.The fourth chapter discusses the asymptotic estimation problem of ruin probability due to the multi-risk perturbed model with investment income. By establishing independent multi-risk perturbed model, the asymptotic estimation of finite-time ruin probability and infinite-time ruin probability is derived.