Research On Ruin Probabilities And It’s Asymptotic Relationship In The Two Types Of Delayed Renewal Risk Models

The core question of the risk theory is the insurance company’s ruin probability.The heavy-tailed distribution problem has become an increasingly hot topic in recentyears because it can describe the extreme events well. In this paper, we investigate theruin probability for two types of delayed renewal risk models with constant interestforce. In the models, the claims from a sequence of identically distributed randomvariables with heavy-tailed distribution.This paper contains four chapters.In chapter1, the background and the main work of this paper are introduced.In chapter2, first, it gives a brief introduction about the classical Poisson modeland its ruin probability. Then it gives the definition of the heavy-tailed distribution、several important distribution groups and the relationship among of them.In chapter3, we use some negative dependent claims instead of the independentclaims. In the delayed renewal model, when the claims obey the identical distributionERV, we obtain the asymptotic expression of the ruin probability:In chapter4, we discussed a new risk model, which is called delayed compoundrenewal risk model. It assumes that at the same time the insurance company has morethan one customer need to claim. Obviously, this model is closer to the actual. In thismodel, when the claims are independent and obey the subexponential distribution, weobtain the asymptotic expression of the ruin probability:...