The Problems Of Periodic Dividend And Ruin About The Classical Risk Model With Interest

The risk theory mainly studies the stochastic risk model relating to the insurance and finance,and analyze the security of insurance company operation from a.quantitative point of view.So it's a heat subject in actuary and mathematics research.Ruin theory is the core of the risk theory.The study of ruin theory has practical background and probability meaning.As for the another important part,dividend problem reflects the real operation state of the company.With the developing of the science and technology and the improvement of the mathematics,more and more risk models and dividend strategies are presentedThis paper studies the classical risk process model with interest,that is:Based on this model,we consider the random dividend strategy,that is only in the stochastic dividend time and the surplus of insurance company exceeding b can we pay the dividend to the shareholders.Considering the random dividend strategy,this paper studies two kinds of ruin problems.What is one of them is the traditional ruin.Firstly,we deduce that tho experted discounted dividend function VO(x,b)satisfies the following integro-differential equations:when 0? x<bwhen x ? bSecondly,we deeduce that the Gerber-Shiu function ?0(x,b)satisfies the following intogro-differential equations:when 0 ?x<bwhen x ?bThirdly:we assume that the claim subjects t.o the exponential distribution,whose pa-rameter is ?(?>0),or f(y)= ?e-?y.Then we obtain the solutions of Vo(x,b)and ?0(x,b)respectively.Lastly,we get separately the following integro-differential equations that the moment generating function M0(x,y,b)and m.-th monments V0m(x,b)of D0 satisfy:when 0?x<b and when x? b andThe second one is the absolut,e ruin.Being silmilar to the traditional ruin,we derive all the integro-differential equations separately every relative object satisfied.