不完备市场上基于虚拟证券的鞅测度  

Martingale measure based on virtual securities in incomplete market

作　　者：朱捷 王生喜 王杰 ZHU Jie;WANG Sheng-xi;WANG Jie(Guangdong University of Science and Technology,Dongguan 523083,China;Tan Kah Kee College,Xiamen University,Zhangzhou 363105,China)

机构地区：[1]广东科技学院,广东东莞523083 [2]厦门大学嘉庚学院,福建漳州363105

出　　处：《哈尔滨商业大学学报（自然科学版）》2022年第5期604-609,632,共7页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：广东科技学院科研项目(GKY-2021KYYBK-34).

摘　　要：基于多维扩散过程所驱动的不完备市场,引入虚拟证券,研究了不同准则下的最优鞅测度问题.首次提出了均方误差次优准则及相对均方差次优准则,并在上述两个准则下,得到了鞅测度的显式表达,验证了上述鞅测度在二阶矩意义上与极小鞅测度、相对熵极小鞅测度以及方差最优鞅测度无差异.Based on the imperfect market driven by multidimensional diffusion process,the optimal martingale measure under different criteria was studied by introducing virtual securities.The mean square error suboptimal criterion and the relative mean square error suboptimal criterion are proposed for the first time.Under the above two criteria,the explicit expression of martingale measure was obtained.It was verified that the martingale measure mentioned above was no different from the minimum martingale measure,the relative entropy minimum martingale measure and the variance optimal martingale measure in the second moment sense.

关 键 词：不完备市场 虚拟证券 最优鞅测度 未定权益 对冲策略 

分 类 号：O211.63[理学—概率论与数理统计]