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

YUN Tian-quan; LEI Guang-long

Volume 24 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(6): 579-582

YUN Tian-quan, LEI Guang-long. Simplest Differential Equation of Stock Price,Its Solution and Relation to Assumption of Black-Scholes Model[J]. Applied Mathematics and Mechanics, 2003, 24(6): 579-582.

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

YUN Tian-quan¹,
LEI Guang-long²

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

Received Date: 2002-02-06
Rev Recd Date: 2003-02-19
Publish Date: 2003-06-15

Abstract

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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