Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 6, Issue 2


Published
on

December 13, 2021


Pages

91-102


DOI

Article

Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets

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Authors

Limin Tao Affiliation:
Xianda College of Economics and Humanities Shanghai International Studies University, Shanghai 200083, China
, Liping Xu Affiliation:
Shanghai Branch, HNA Futures Company Limited, Shanghai 200122, China
and Hani Jamal Sulaimani Affiliation:
Department of Computer Information Systems, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia


Abstract

The pricing and hedging of financial derivatives have become one of the hot research issues in mathematical finance today. In the case of non-risk neutrality, this article uses the martingale method and probability measurement method to study the pricing method and hedging strategy of financial derivatives. This paper also further studies the hedging strategy of financial derivatives in the incomplete market based on the BSM model and converts the solution of this problem into solving a vector on the Hilbert space to its closure. The problem of space projection is to use projection theory to decompose financial derivatives under a given martingale measure. In the imperfect market, the vertical projection theory is used to obtain the approximate pricing method and hedging strategy of financial derivatives in which the underlying asset follows the martingale process; the projection theory is further expanded, and the pricing problem of financial derivatives under the mixed-asset portfolio is obtained. Approximate pricing of financial derivatives; in the discrete state, the hedging investment strategy of financial derivatives H in the imperfect market is found through the method of variance approximation.


Keywords

B-S-M model, nonlinear differential equation, financial market, financial derivatives, 62J12


Citation

Tao, L., Xu, L., & Sulaimani, H. J. (2021). Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets. Applied Mathematics and Nonlinear Sciences, 6(2), 91–102. https://doi.org/10.2478/amns.2021.2.00070

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