非完备市场欧式期权无差别定价研究
发布时间：2018-10-08 17:14
【摘要】：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.
[Abstract]:This paper deals with the optimal consumption / investment decision and option pricing under the criterion of maximizing expected consumption utility in incomplete markets. On the assumption that the underlying asset price changes back from the geometric mean, By using stochastic dynamic programming theory and the principle of non-differential pricing of consumption utility, the partial differential equations of optimal consumption / investment strategy and non-tradable European option price of underlying assets are obtained. A numerical example is given. The results show that the investor's risk-aversion attitude will reduce the utility price of the option, while the average return property of the underlying asset makes the variation of the option price with time controlled by the equilibrium price level of the underlying asset. There are two different trends of monotone increasing and monotone decreasing.
【作者单位】： 湖南大学金融与统计学院;南京审计学院数学与统计学院;南京审计学院金融学院;
【基金】：国家自然科学基金资助项目(70971037) 江苏省高校青蓝工程项目 南京审计学院青年课题资助项目(NSK2009/C06)
【分类号】：F830.9;F224
本文编号：2257602
[Abstract]:This paper deals with the optimal consumption / investment decision and option pricing under the criterion of maximizing expected consumption utility in incomplete markets. On the assumption that the underlying asset price changes back from the geometric mean, By using stochastic dynamic programming theory and the principle of non-differential pricing of consumption utility, the partial differential equations of optimal consumption / investment strategy and non-tradable European option price of underlying assets are obtained. A numerical example is given. The results show that the investor's risk-aversion attitude will reduce the utility price of the option, while the average return property of the underlying asset makes the variation of the option price with time controlled by the equilibrium price level of the underlying asset. There are two different trends of monotone increasing and monotone decreasing.
【作者单位】： 湖南大学金融与统计学院;南京审计学院数学与统计学院;南京审计学院金融学院;
【基金】：国家自然科学基金资助项目(70971037) 江苏省高校青蓝工程项目 南京审计学院青年课题资助项目(NSK2009/C06)
【分类号】：F830.9;F224
【二级参考文献】
相关期刊论文 前1条
1 杨招军;部分信息下极大化终止时刻期望效用[J];控制理论与应用;2005年05期
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