The Risk Model With Dividend Barrier

As a kind of new life insurance product,participating insurance has its own advantages and thus is welcomed by the consumers home and abroad.Many insurance companies take it as their main service product,and get high premiums.But on the other hand,participating insurance has some problems and so it becomes one of the hot topics experts study.Participating insurance was first put forward by De finetti in 1957,and scholars such as Gerber and Shiu have made deep research.On the base of previous researches,this thesis studies two models of participating insurance:One is the risk model with interest and a Threshold dividend strategy.The reason why the factor of interest rate is introduced is that,since the interest rate was determined by the market, while the risk of interest rate has significant impact on participating insurance products.Under the Threshold dividend strategy,if the surplus of an insurance company is not more than a given level b,then the dividends are not paid;On the other hand,if the surplus reaches the given level b,then the dividends are paid by this formula:a +δb(a＝c ),δis the interest force.This thesis gets the integro-differential equations for the Gerber-Shiu discounted penalty function,the solve of the equations,and also gets the integro-differential equations for the expectation present value function of dividend payments.The second model is the risk model with stochastic premium and linear dividend barrier. In the classical risk model,the premium is collected on unite time basis,but in reality,the collecting of premiums should be random,so in this part set the times of collecting premiums as a Poisson process,and make the model more realistic.In this model,set up a linear dividend barriery,=b+at,where b is an initial value(u≤b),a is a speed(0＜a＜λ₁p₁). Thus,if the surplus is less than the dividend barrier,the dividends are not paid.As long as the surplus is more than the dividend barrier,the dividends are paid.This thesis gets the integro-differential equations for the expectation present value function of dividend payments and the discounted penalty function.