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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,建立在累积赔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.
Insurance pricing in the complete market is more familiar to people, but it is not in line with the actual market.This paper studies the problem of insurance pricing in the incomplete market.Through the analysis of accumulated insurance losses, the insurance pricing under cumulative claims Model.An investment model of insurance investment is established based on the investment of a riskless asset and a limited number of risk assets.By means of deformation, the backward stochastic differential equation of the insurance price is obtained, and by using the theory and method of backward stochastic differential equation, The corresponding formula of insurance price is obtained.Finally, an example is given to analyze.The research in this paper, without considering the factors such as the death rate and the probability distribution of loss, provides a new idea for insurance pricing and enriches the limited insurance pricing method .