<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

Xianda College of Economics and Humanities Shanghai International Studies University

Department of Computer Information Systems, Faculty of Computing and Information Technology

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

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,...

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

Published Online: Dec 13, 2021

Page range: 91 - 102

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00070

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

© 2021 Limin Tao et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: Dec 13, 2021

Page range: 91 - 102

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00070

KeywordsB-S-M model, nonlinear differential equation, financial market, financial derivatives

© 2021 Limin Tao et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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