Study On The Asymptotic Estimate Of Ruin Probability In Different Risk Models

Risk theory is a hot topic in the present actuarial science and mathematics research. Byusing stochastic processes theory, the classical risk theory studies mainly the surplus processof single-insurance, ruin time,ruin probability and adjustment coefcient. With the scale ofthe business expanding incessantly and the types of insurance increasing,there are obviouslimitations of e classical risk model. So there is a vast of literatures devoted into modifyingthe model and made the model more power in describing the practical world.In insurance mathematics, ruin theory is the mainly contents of insurance risk theory,as can supply a very useful early-warning measure for risk of the insurance company. Inthis dissertation, under the classical risk model,consider a variety of factors,we get somegeneralized risk model by extends the time interval sequenceàcliams process and so on,and gives a through research of ruin probability and absolute ruin probability under thesemodels. The thesis includes four chapters.In chapter1, we introduces the evolutional course and actuality of risk model, expoundedthe direction, content and significance of this thesis.In chapter2, we imports the classical risk model, introduce the diferent risk models andgives some definitions of the distribution with heavy tailed.In chapter3, we mainly give the compound Poisson risk model and the renewal riskmodel with constant interest force,under this model,use the method of renewal function andconvolution,studied the situations of the claim distribution with heavy tail, we present theasymptotic properties of ruin probability and the ultimate ruin probability under the riskmodel with constant interest force.In chapter4, We use the method in the third chapter,extend to the renewal risk modelwith constant interest force,and gives the properties of absolute ruin probability when theinitial surplus tends to infinity.