Application of Moore-Penrose Inverse in Deciding the Minimal Martingale Measure

作者：Yao, Luo-gen^*; Yang, Gang; Yang, Xiang-qun

来源：Acta Mathematicae Applicatae Sinica-English Series, 2010, 26(4): 653-660.

DOI：10.1007/s10255-010-0030-1

• Moore-Penrose inverse
• minimal martingale measure
• semi-martingales
• structure condition

The Moore-Penrose inverse is an important tool in algebra. This paper shows that the Moore-Penrose inverse is also an efficient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure condition. We extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still predictable. Furthermore, we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose inverse. Specifically, the minimal martingale measure in a generalized Black-Scholes model is found.

• 出版日期2010
• 单位湖南师范大学; 湖南商学院