The Study Of Problems For Dividends And Ruin On Two Kinds Risk Models

This paper is divided into three main parts. The first part mainly studies the dividends of the compound Possion model perturbed by diffusion, and consider it by the threshold dividend strategy. Using compound Possion process to approach Brownian motion, unifing the conclusion which Gerber and Shiu(2006) given, we get until all bankruptcy of the expected dividend present discount V(x, b) of inter-differential equationsAnd gives the exact expression of V(x,b), when moment generation function satisfy certain conditions.The second part mainly studies the Erlang(2) risk model under constant interest force, combines with the multi-divided strategy, and gives the inter-differential eqution about the Gerber-Shiu discounted penalty function Furthermore, when the claimsize is exponentially distributed, a differential equations can be derived.In the third part, we investigate the moments of the surplus before ruin and the deficit at ruin under the former conditions. And we obtain integral equation that F(u,x), G(u,x), H(u,x,y) satisfiedAnd its precise solutions are also given.