Research On The Risk Model Under The Linear Barrier Dividend

Dividend theory and dividend strategy in risk theory are hot topics in current actuarial research.The first dividend strategy is the barrier strategy.However,if the barrier strategy is implemented,it will eventually lead to the bankruptcy of the insurance company.In 1974 Gerber proposed a time-dependent barrier of type b(t)=b+at,a>0,b>0.Whenever the surplus X(t)reaches b(t),then the dividends are paid out to the shareholders and the surplus remains on the barrier until the next claim occurs,otherwise there is no dividend.The risk model of the linear barrier dividend strategy is closer to the changing rules of the real market,and it can effectively control the risk,which is more realistic.This paper mainly studies double compound Poisson risk model and the classical risk model under the linear barrier dividend strategy.Several results of the corresponding model are obtained,which are shown in the following aspects:Chapter 1 is the introduction,introducing the current situation and research background of risk model and dividend strategy.Furthermore,we make an outline of the main research work of this paper.Chapter 2 studies the linear barrier dividend in the double compound Poisson risk model.We derive the integral-differential equation that the expected discounted dividend function V(x,b)satisfies:???And we derive the integral-differential equation that the Gerber-Shiu function m(x,b)satis-fies:???Chapter 3 studies the dividend problem of the classical risk model under the periodic linear barrier dividend strategy.Firstly,we derive the integral-differential equation that the dividend payments continued after ruin W(u),u=b-x satisfies:???When the amount of claim is subject to the exponential distribution,we obtain the solutions of W(u),Secondly,we derive the integral-differential equation that the dividend payments stopped at ruin V(x,b)satisfies:???When the amount of claim is subject to the exponential distribution,we obtain the solutions of V(x,b).Lastly,we derive the integral-differential equation that the ruin probability ?(x,b)sat-isfies:???Chapter 4 summarizes the paper.