不完全市场的保险定价研究

完全市场上的保险定价问题是人们比较熟悉的研究内容,但它不符合市场实际.本文在不完全市场上研究保险定价的问题.通过对累积保险损失的分析,建立在累积赌付下的保险定价模型;基于对一个无风险资产和有限多个风险资产的投资,建立保险投资定价模型.通过变形,得到相应的保险价格的倒向随机微分方程,并利用倒向随机微分方程的理论和方法,得到了相应的保险价格公式.最后,给出释例进行了分析.本文的研究,不用考虑死亡率、损失的概率分布等因素,为保险定价提供了新的思路,丰富了有限的保险定价方法.

Research on Insurance Pricing in an Incomplete Market

The problem of insurance pricing is understood in the contest of a complete market, but the hypothesis on complete is not correspond to real market. This paper studies the problem of insurance pricing in an incomplete market, throught analysis of insurance aggregate claims, insurance pricing model is established in the condation of insurance aggregate claims,and with investment in assets containing a free-risk bond and a finite number of stocks whose prices are drives by Brownian motion process, insurance investment pricing model is established. Using a way to complete the market, and insurance pricing model and insurance investment pricing model is obtained, and models are deformed to backward stuchastic differential equations of insurance pricing and insurance investment pricing, using theory and mothed of backward stuchastic differential equations, formula for insurance price are given. Final, example is studied in detail. In this paper, the insurance pricing method need not to consider the mortality rates and the probability distributionof losses. The insurance pricing method provides a new thinking for insurance pricing, enrich insurance pricing methods.