股价最简微分方程,其解及与Black-Scholes模型的假设的相互关系

基金项目: 湖南省科委软科学基金资助项目(02ZRN2030)

Simplest Differential Equation of Stock Price,Its Solution and Relation to Assumption of Black-Scholes Model

1.
Department of Mechanics, South China University of Technology, Guangzhou 510641, P. R. China;
2.
College of Administration of Industry & Commerce, Hunan University, Changsha 410082, P. R. China

摘要: 在系数的某种等价关系条件下,股价的两类数学表达式,一类是基于明确型描述的由类似固体力学方法导出的最简微分方程(S.D.E.)的解,另一类是基于不确定型描述(即统计理论)的Black-Scholes模型的假设(A.B-S.M.),即股价密度函数服从对数正态分布,可以是完全相同的.S.D.E.的解仅适用于股市的常规情形(无利好或利空消息,等),因此,A.B-S.M.的适用范围也相同.
- 股票市场 /
- 期权定价 /
- Black-Scholes模型 /
- 概率与确定性 /
- 微分方程
Abstract: Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation(S. D. E.) obtained by method similar to that used in solid mechanics, the other based on uncertain description(i. e., the statistic theory)is the assumption of Black-Scholes s model(A. B-S. M.) in which the density function of stock price obeys logarithmic normal distribution, can be shown to be completely the same under certain equivalence relation of coefficients. The range of the solution of S. D. E. has been shown to be suited only for normal cases (no profit, or lost profit news, etc.) of stock market, so the same range is suited for A. B-S. M. as well.
- stock market /
- option pricing /
- Black-Scholes model /
- probability and certainty /
- differential equation

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