The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-m...The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient 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.展开更多
基金Supported by the National Natural Science Foundation of China (No.10871064)the Key Laboratory of Computational and Stochastic Mathematics and It's Applications,Universities of Hunan Province,Hunan Normal University and the Soft Scientific Research Funds of Hunan Provincial Science & Technology Department of China (No.2009ZK4021)
文摘The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient 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.
