Absolute Ruin Probability Based On Poisson Distribution With Interference And Dividend Strategy Of Multiple Threshold

The classical risk models and a variety of promotion risk models considering the variable characteristics of ruin probability as theoretical basis can't make it better to predict and control ruin for insurance companies. But the study found that the absolute ruin probability is a better instrument for the insurance companies to have better prevention and control of the ruin. In addition, the dividend strategy of the insurance risk model as one of the current research has drawn people's attention. Since1857Di Fineth proposed the dividend strategy, a large number of scholars on the risk model with dividend strategy conduct many studies, including two of the most popular dividend strategy which are dividend strategy and threshold dividend strategy. Barrier dividend strategy indicates the insurance company sharing all the surplus as an extra dividend to shareholders when surplus exceeds a certain constant; threshold dividend strategy indicate that the insurance company will share the part of surplus exceed a certain constant to shareholder by proportion when surplus exceed the constant.Recently, multiple threshold dividend strategy, as one of the current research's focus has drawn people's more and more attention. First of all, we propose a class of poisson risk model with interference and multiple threshold dividend strategy on the basis of existing theory; Second, the paper derives the Piecewise integral differential equation and Piecewise exponential integral equation satisfied by Gerber-shiu expected discounted penalty function by Lapbare transform. Third, we further seek the exact expression of the expected discounted penalty function when claims obey the exponentially distributed and research of the absolute probability problem of this model.