Application Of Renewal Theory In Non-life Insurance

This article is based on application of renewal theory in Non-life insurance.Beginning from the surplus process,we study accuracy quantities that connect withruin probability.Then we found on several renewal equations and integro-differentialintegral equation.Using differential and integrated method and Laplace transformationways， we derive some properties of the quantity such as the explicit expression，asymptotic form and bounds.We study the moments of ruin time in the renewal risk model of inter-arrivaltime of Erlang(3) distribution.Ruin probability of finite time in renewal risk model ofhomogenous poission distribution or random investigation,the joint distribution ofprior to and at ruin for the finite-time ruin.finite-time ruin probability forsubexponential claim size in dependent risk model.Renewal equation exists in all kinds of risk model in renewal Process. It is veryimportant to find and solve the renewal equation.Reading the paper, we will not hardlyfind，(defective) renewal equation can solve by the Renewal Theorems， and also byLaplace transform.Some large claim need to describe by heavy tailed distribution， themore we study the heavy-tailed property,the explicitly the expression of our ruinprobability.