The Research On The Classical Dividend Strategy In Risk Theory

The division of dividend in insurance companies has been widely concerned. The article is devoted to this problem from the point of the strategies of the division of dividend, which is the dividend barrier strategy. The article has mainly studied two kinds of dividend strategies based on the risk theory, one of which is constant dividend barrier strategy, the other linear barrier strategy. In the constant threshold barrier strategy, if a barrier strategy with parameter b is applied, no dividends are paid while the surplus is below b, and the overflow with respect to the level b is paid as dividends. Whever the free reserve reaches a linear barrier b+at, dividends are paid out in such a way that the reserve stays on the barrier with intensity less than premium density in the linear barrier strategy.1. We get the Integro-differential equations with certain boundary conditions for the expectations of the discounted dividend payments, discounted deficit , life of an insurance company,of the discounted dividend payments at ruin are derived and solved in the constant barrier strategy perturbed by diffusion.2. We generalize to linear barrier strategy perturbed by diffusion, and the Integro-differential equations with certain boundary conditions for the expectations of the discounted dividend payments, discounted deficit, life of an insurance company, the discounted dividend payments at ruin and the moment-generating functions of the sum of the discounted dividend payments both at ruin and after ruin are derived and solved.3. Under the case of constant dividend barrier model with investment, we derived the Integro-differential equations with certain boundary conditions for the expectations of the discounted dividend payments, life of an insurance company,ruin probability, the discounted penalty function of the sum of the discounted dividend payments are derived and solved.The last chapter is divided into 4 parts, we generalize the meanings, functions of participating insurance, dividend assignment principle and ways.