Martingale Analysis And Ruin Probability For Two Kinds Of Generalized Poisson Risk Model

The policy-holder investment strategy is an important factor for investment risk.The famous Cramer-Lundberg model is proposed to compute investment strategyand ruin probability, which is a main problem in studying risk model. Martingale is afrontier theory to study a random process. It has the advantages like deepness andconciseness. Therefore, using martingale theory to study various risk models is ofgreat importance to improve the financial market and expand the investmentenvironment for Policy-holders. After summarizing the former works, this paperintroduces the bankrupt lower limit function into the generalized Poisson risk modeland discusses the ruin probability of the risk model when the lower limit functiondoes not tend to zero. What’s more, creating an investment environment in whichpremium income is always greater than claims expenditure and proposing the beststrategy for the reinsurance business are also main tasks of this paper.Firstly, this paper reviews the research situation for the martingale method andinvestment risk models. Related concepts and theories are stated. The classicCramer-Lundberg model is discussed. Research methods and ruin probabilities forvarious risk models are elaborated.Secondly, the basic theories of martingale analysis related to risk models arestated. After studying a great amount of materials, the former risk models aresummarized. However, in a changing market operation, discussing the variousfactors which influence the investment of policy-holders, such as the influence of theoperation scale and the development of new insurances on the policy-holders, thefluctuations of bank interest rates, and other factors is essential. Developing a newmodel is of vital importance. In this paper, the classic Poisson risk model isdeveloped on two aspects to make it fit the market better. Thirdly, in the practical market, an insurance company will not wait to adjustthe policy when bankrupt really occurs. When earning is below a certain limit, theinsurance company will adjust the policy to prevent bankruptcy. This paper assumesthe bankruptcy lower limit is a function of time. With the expansion of the insurancecompany, discussing the bankruptcy problem of risk process becomes more andmore important. Considering these two points, the composite double Poisson riskmodel is proposed in this paper. The martingale stopping theorem is used to derivethe generalized composite double Poisson risk model when the lower zero functiondoes not tend to zero. This model fits the market environment better and provides amore liberal investment environment for policy-holders. What’s more, a promotedPoisson risk model is concerned in this paper, which defines a safety upper and abankruptcy time. A new risk model is established, which makes the premium incomeis always greater than the claims expenditure. The best strategy for the reinsurancebusiness is proposed. The upper and the inequalities for the ruin probability arecomputed, which is of great practical significance.