The Study Of Heavy-Tailed Distribution And Its Application In Estimation Of The Ruin Probabilities In Risk Model

Ruin theory is an important part of Actuarial Mathematics, which not only has important theoretical research value, but also has a strong practical value in the risk management of insurance companies. As one of the four pillars of the financial sector, the insurance industry itself also faces the risk of claims, especially the "large claims", which has a significant impact on the company’s operating, we use heavy-tailed distribution to describe such claims in mathematics. The Lundberg-Cram-er classical risk model does not consider the impact force of interest factors, but the force of interest has an important influence on investors’ decision-making and investment behavior under the market economy environment, it is an important considerable factor to the insurance company.The content of thesis is the ruin probability of discrete time risk model with interest force factors considered under heavy-tailed claims. The full thesis divides into five chapters:The first chapter is the introduction, we mainly introduces the development history of ruin theory and the Lundberg-Cramer classical risk model, and summarizes the risk models which are generalized or improved by the scholars. Finally, we summarize several representatives the research direction of contemporary ruin theory. The second chapter is the heavy-tailed distribution and its subclasses, we introduce the definition of heavy-tailed distribution and the division of its subclasses and also we study the relationship between heavy-tailed distributions.In the third chapter we consider the discrete time risk model with variable interest force, which are deformated by surplus discounted. Assuming that the individual net risk belong to D∩L family and εRV family, we obtain asymptotic estimation of finite and infinite time ruin probability and its upper and lower bounds.In the fourth chapter we consider the discrete time risk model with Markov chain interest force. Assuming individual net risk obey R-α family and related heavy-tailed assumptions, using the total probability formula and the recursive method, we obtain the approximate expression of ruin probability in finite time discrete risk model.In the fifth chapter we summarize the study results and introduce the next step work plan of the author.