山西大学学报（自然科学版）2008，Vol.31Issue(3)：418-424,7.
M-P逆与一般B-S模型中的等价鞅测度
Moore-Penrose Pseudo-Inverse and Equivalent Martingale Measures in General Black-Scholes Model
摘要
Abstract
To find an equivalent martingale measure in General Black-Scholes model,we need to solve the market price of risk equations firstly.However,classical methods always assume the dispersion matrix is full rank almost surely when deriving a specific market price of risk.By Moore-Penrose pseudo-inverse theory in algebra,this paper proofs that Moore-Penrose pseudo-inverse method is an efficient technique to solve the market price of risk even if the dispersion matrix is not always full rank.According to the criterion that minimizes the Frobenius norm of market price of risk,we can find a unique equivalent martingale measure by virtue of the Moore-Penrose pseudo-inverse of dispersion matrix.It goes to prove that our equivalent martingale measure is the same as the Esscher transformed martingale measure,the minimal entropy martingale measure and the minimal reverse entropy martingale measure under the certain conditions in General Black-Scholes model.关键词
M-P逆/一般B-S模型/等价鞅测度/期权定价Key words
Moore-Penrose pseudo-inverse/General Black-Scholes model/equivalent martingale measure/option pricing分类
数理科学引用本文复制引用
姚落根,杨向群..M-P逆与一般B-S模型中的等价鞅测度[J].山西大学学报（自然科学版）,2008,31(3):418-424,7.基金项目
Supported by National Nat ural Science Foundation of China (10571051) （10571051）
