Ruin Probability And Numerical Simulation Of Heavy-tailed Claims Risk Model

Investigated in this paper is the ruin probability of heavy-tailed claims risk model andthe corresponding numerical simulation. In the fnance and insurance sector, the mainobject of study is the large claims arising from catastrophic events, which will bring asignifcant risk for the insurance business once occured, may make the insurance companyinto a fnancial crisis, even bankruptcy. In recent years, these phenomena have been con-cerned by many scholars, and they are trend to research the ruin probability. With theeforts of many scholars, they get asymptotic formula under diferent conditions.However,these results mostly are theoretical, lack practical signifcance. Recently, many researchershave not satisfy only stay on the theoretical results, but to verify the reasonableness of the-oretical, and has made good progress. This article has not only theoretical breakthrough,but also make matlab simulations, which verify the reasonableness of the theory.In addition, we consider the heavy-tailed phenomenon and the dependency among theclaim size in this paper. In recent years, scholars research on the theory of insurance riskmore concentrated in the dependency case. In this paper, the results will also be extendedto the dependency theory, that is, in the special case of the upper-tailed dependent–upper-tailed independent, which make the description of claim size more practical.This paper consists of three parts.First chapter introduces the classical risk model and its extended form, draw a diagramof the surplus process under various conditions, and compared them each other.In the second chapter the main content is ruin probability of heavy-tailed potentialclaims risk model and numerical simulation. In the case of the claim size belongs to classS, an asymptotical equality formula of the fnite-time ruin probability is obtained, thesimulation results are given.Third chapter research the ruin probability for risk model with upper-tailed indepen-dent heavily-tailed prospective claims, assuming that the claim sequence is upper-tailedindependent and have same heavy-tailed distributions. The condition that the claim sizebelongs to class L∩D, an asymptotical equality formula of the fnite-time ruin probability is obtained.