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Applied Mathematics and Mechanics

, Volume 24, Issue 6, pp 654–658 | Cite as

Simplest differential equation of stock price, its solution and relation to assumption of black-scholes model

  • Yun Tian-quan
  • Lei Guang-long
Article

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 mechnics, 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.

Key words

stock market option pricing Black-Scholes model probability and certainty differential equation 

Chinese Library Classification

F830.9 

2000 MR Subject Classification

91B28 91B64 

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Yun Tian-quan
    • 1
  • Lei Guang-long
    • 2
  1. 1.Department of MechanicsSouth China University of TechnologyGuangzhouP. R. China
  2. 2.College of Administration of Industry & CommerceHunan UniversityChangshaP. R. China

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