非完备市场欧式期权无差别定价研究

摘要

The problem of optimal consumption/investment and option pricing for maximizing the expected consumption utility in an incomplete market was studied. Under the assumption that the underlying asset is non- traded and follows a mean-reverting process, we obtained the optimal consumption and investment strategy* together with a partial differential equation for the European option pricing by stochastic dynamic programming and consumption utility indifference pricing principle. Numerical examples were presented. The results indicate that risk aversion will decrease option price, which changes with time but also depends on the mean reverting level under such model, I. E. According to two different cases the option price may increase or decrease with time respectively.%研究不完备市场中最大化期望消费效用准则下的最优消费/投资决策及期权定价问题.在标的资产价格服从几何均值回复变化的假设下,利用随机动态规划理论及消费效用无差别定价原理得到了最优消费/投资策略以及标的资产不可交易的欧式期权价格所满足的偏微分方程.给出了数值算例,结果表明投资者的风险厌恶态度会降低期权的效用价格,而标的资产的均值回复特性使得期权价格随时间的变化规律受控于标的资产均衡价格水平,分情况可表现出单调递增和单调递减的2种不同变化趋势.