Several Types Of The Risk Model Of Generalized Fine Discount Expect Function Analysis

Since1998, the expected discounted penalty function was first proposed by Gerberand Shiu, so the actuarial amount have been studied by many scholars. At the sametime, many scholars gave the improvement about this actuarial amount. For example,Cheung et al.(2010) studied the generalized expected discounted penalty function of theclassical risk model. The actuarial amount adds to an random variables of the surplusimmediately after the penultimate claim befor ruin occurs. This thesis is a continuationof this research. The gnenralized expected discounted penalty function of three classes ofrisk model are studied. The first is the classical risk model with tax; The second is therisk model driven by a subordinator; The last one is the risk model with random income.This thesis is divided into four chapters.Chapter1is preface. We introduce the background of the generalized expecteddiscounted penalty function.In chapter2, we get an integro-diferential equation for the generalized expecteddiscounted penalty function of the classical risk model with tax.In chapter3, we give the equation and an ininite series expression of the generalizedexpected discounted penalty function of the risk process driven by a subordinator.For δ≥0, an equation of the generalized expected discounted penalty function inclassial risk model as follows: In chaper4, we give the defective renewal equation for the generalized Gerber-Shiufunction when the random income is a combination of exponential distributions.When δ>0, the defective renewal equation of the generalized expected discountedpenalty function φ(u) as follows:...