SIMPLEST DIFFERENTIAL EQUATION OF STOCK PRICE,ITS SOLUTION AND RELATION TO ASSUMPTION OF BLACK-SCHOLES MODEL

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (6): 654-658.

SIMPLEST DIFFERENTIAL EQUATION OF STOCK PRICE,ITS SOLUTION AND RELATION TO ASSUMPTION OF BLACK-SCHOLES MODEL

云天铨¹, 雷光龙²

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

收稿日期:2002-02-06 修回日期:2003-02-19 出版日期:2003-06-18 发布日期:2003-06-18
基金资助:
the Foundation Fund of Soft Science of Hunan Province(02ZRN2030)

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:2002-02-06 Revised:2003-02-19 Online:2003-06-18 Published:2003-06-18
Supported by:
the Foundation Fund of Soft Science of Hunan Province(02ZRN2030)

摘要/Abstract

摘要： 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.

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.

中图分类号:

F830.9

云天铨;雷光龙. SIMPLEST DIFFERENTIAL EQUATION OF STOCK PRICE,ITS SOLUTION AND RELATION TO ASSUMPTION OF BLACK-SCHOLES MODEL[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(6): 654-658.

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 (English Edition), 2003, 24(6): 654-658.

参考文献

[1] QIAN Ke-tong.The Authoritative Guide to Contemporary Investment Theories[M].Hong Kong: Hong Kong Publication Group Co Ltd,1990,1-25.(in Chinese)
[2] Ghaziri H,Elfakhani S,Assi J.Neural networks approach to pricing options[J].Neural Network World,2000,(1/2):271-277.
[3] XIE Su.Barrier options pricing of process of constant elasticity of variance(CEV)[J].Journal of Management Science,2001,4(5):13-20.(in Chinese)
[4] QIAN Li.Comment on the major development of theories of options pricing[J].Economic Sci ence,2000,(4):89-97.(in Chinese)
[5] LIU Yan-yan.Probability and Deterministic Theory[M].Shanghai:Shanghai Social Science Pub lishers,1996,6.(in Chinese)
[6] YUN Tian-quan.A basic integro-differential equation of RCPS[J].Journal of South China Uni versity of Technology,1996,24(6):35-39.(in Chinese)
[7] YUN Tian-quan.Short range forecasting of stock price in normal case[J].Journal of South China University of Technology,1997,25(5):47-51.(in Chinese)
[8] YUN Tian-quan.Basic equations,theory and principle of computational stock market(Ⅰ)Basic equations[J].Applied Mathematics and Mechanics(English Edition),1999,20(2):154-162.
[9] YUN Tian-quan.Basic equations,theory and principle of computational stock market(ò))Basic principles[J].Applied Mathematics and Mechanics(English Edition),1999,20(7):721-728.
[10] YUN Tian-quan.Basic equations,theory and principle of computational stock market(ó))Basic theories[J].Applied Mathematics and Mechanics(English Edition),2000,21(8):861-868.
[11] YUN Tian-quan.Analysis of financial derivatives by mechnical method(Ⅱ)Basic equation of price of index futures[J].Applied Mathematics and Mechanics(English Edition),2001,22(1):118 -125.
[12] YUN Tian-quan.Analysis of financial derivatives by mechnical method(ò))Basic equations of market price of option[J].Applied Mathematics and Mechanics(English Edition),2001,22(9): 1004-1011.
[13] YUN Tian-quan.The applications of game theory in stock/options trading[J].Forecasting Jour nal,2001,20(5):36-38.(in Chinese)
[14] Eds of/Mathematical Handbook0.Mathematical Handbook[M].Beijing:Higher Educational Pub lishing House,1979,798.(in Chinese)

SIMPLEST DIFFERENTIAL EQUATION OF STOCK PRICE,ITS SOLUTION AND RELATION TO ASSUMPTION OF BLACK-SCHOLES MODEL

SIMPLEST DIFFERENTIAL EQUATION OF STOCK PRICE,ITS SOLUTION AND RELATION TO ASSUMPTION OF BLACK-SCHOLES MODEL

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	闫海峰;刘三阳. NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(7): 826-835.
[2]	云天铨. ANALYSIS OF FINANCIAL DERIVATIVES BY MECHANICAL METHOD (Ⅱ)-BASIC EQUATION OF MARKET PRICE OF OPTION[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(9): 1004-1011.
[3]	云天铨. ANALYSIS OF FINANCIAL DERIVATIVES BY MECHANICAL METHOD (Ⅰ)-BASIC EQUATION OF PRICE OF INDEX FUTURES[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(1): 118-125.