模糊随机不确定环境下考虑决策者主观判断的亚式期权定价  

Pricing Asian Options under Uncertain Environment with Fuzziness and Randomness Considering Decision Maker’s Subjective Judgment

作　　者：王献东[1,2] 何建敏 WANG Xian-dong;HE Jian-min(School of Sciences,Changzhou Institute of Technology,Changzhou 213032,China;Antai college of Economics and Management,Shanghai Jiao Tong University,Shanghai 200030,China;School of Economics and Management,Southeast University,Nanjing 211189,China)

机构地区：[1]常州工学院理学院,江苏常州213032 [2]上海交通大学安泰经济与管理学院,上海200030 [3]东南大学经济管理学院,江苏南京211189

出　　处：《中国管理科学》2020年第9期33-44,共12页Chinese Journal of Management Science

基　　金：国家自然科学基金面上资助项目(71771147);江苏省高校自然科学研究面上资助项目(18KJB110001)。

摘　　要：考虑金融市场的不确定性包含随机性和模糊性两个方面,把标的资产价格视作一个模糊随机过程,以连续几何平均亚式看涨期权为例运用随机分析和模糊集理论研究了模糊随机不确定环境下的亚式期权定价问题。首先,推导出了亚式期权模糊价格的任意水平截集,并将如何计算给定任一个参考价格的置信度问题转化为求解最优化问题。然后,研究了两种考虑决策者主观判断的亚式期权定价,一是引入模糊目标表示决策者对期权预期价格的满意度,给出可靠度大于决策者满意度的亚式期权预期价格的范围;二是引入悲观-乐观指数表示决策者的悲观程度,基于加权函数和可能性估计测度定义模糊数的可能性均值,得到可能性均值意义下的亚式期权定价公式。最后,给出了一个数值例子说明了模型的可行性和实用性。Option pricing is one of the core issues in financial engineering research.The value of an option depends on the price of the underlying asset during the period of validity.Therefore,it is the basis and key of option pricing to properly construct the underlying asset price dynamic model.The mainstream option pricing model mainly describes the uncertainty of underlying asset price by stochastic differential equations.However,the financial system is highly complex.Owing to market fluctuations,human error,insufficient information and other reasons,the uncertainty cannot be described only by randomness.For instance,if the stock price is around 50 yuan,it is difficult to model the phrase"around 50"from the perspective of probability theory,obviously it has a fuzzy feature.The uncertainty in financial markets involves at least two aspects,namely,fuzziness and randomness,and these two aspects cannot be substituted.Randomness can be modeled by the stochastic analysis theory,and fuzziness can be modeled by the fuzzy set theory.In addition,the recent behavioral financial studies have shown that decision maker’s subjective judgment,such as sentiment,preference and expectation,have a certain impact on decision-making.Based the above analysis,a fuzzy stochastic process model is constructed for underlying stock price by fuzzy random variables,and the stochastic analysis and fuzzy set theory are used to study the pricing problem of continuous geometric average Asian call options under uncertain environment with fuzziness and randomness taking account of investor’s subjective judgment.An Asian option is a popular financial derivative,where the payoff is based on the average underlying asset price over some pre-set period prior to maturity.The payoff structure of Asian options makes them less vulnerable to manipulation.Firstly,the arbitrary level cut sets of Asian option fuzzy price is deduced according to the definition of expectations of fuzzy random variables,and the problem of determining the confidence degree for any giv

关 键 词：亚式期权定价 模糊随机不确定 模糊目标 悲观-乐观指数 可能性均值 

分 类 号：F830.9[经济管理—金融学]