Model Of Classical Risk Process With Threshold Dividend And Tax

This paper considered the ruin probability in a general risk model deriven by acompound Poisson process. In this paper, we consider the classical Cramer-Lundbergrisk model by including loss-carried formula tax payments and threshold dividend.wederive an exact formula for the ruin probability when the claims are exponential andan explicit asymptotic formula when the claims are subexponential,For more we get anintegro-diferential equation for Gerber-Shiu expected discounted penalty function in therisk model,Finally we analyze hou tax payments and threshold dividend afect the behav-ior of a C-L surplus process by defining an expected discounted penalty function at ruin.then, we derive an explicit expression for this function by solving a diferential equation.The thesis is divided into four chapters based on the contents:Chapter1we introduced the Albrecher-Hipp tax identity, gave the Subexponen-tial distributions. Furthermore,we introduce the risk model with tax payments and athreshold dividendMα,γ(s)=max{Rα,γ(s),0≤s≤t}, α>0, b>0are two constants,γ∈[0,1), α≤c(1γ). In this model when Rα,γ(s) run to the maximum, the insurer will pay a taxrate cγ at profitable times, According to such strategy,dividends are paid at a constantrate α whenever the modified surplus is above the threshold b,and no dividends are paidwhenever the modified surplus is below b.In Chapter2, Firstly we introduced the risk model with tax payments and thresh-old(1.2.4).we derive a formula for the ruin probability from which the Albrecher-Hipp taxidentity follows as a special case,then we derive an exact formula for the ruin probability when the claims are exponentialand an explicit asymptotic formula when the claims are subexponentialIn Chapter3, we get the integro-diferential equation satisfied by the Gerber-Shiuexpected discounted penalty function in the risk model.In Chapter4, we analyze hou tax payments and threshold dividend afect the be-havior of a C-L surplus process by defining an expected discounted penalty function atruin.then, we derive an explicit expression for this function by solving a diferential equa-tion.