A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance

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doi:10.3934/mcrf.2019013

Article Contents

2019, Volume 9, Issue 2: 257-276. Doi: 10.3934/mcrf.2019013

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A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance

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1.
Department of Mathematics, Southern University of Science and Technology, Shenzhen, China
2.
Department of Mathematics, University of Macau, Macau, China
3.
School of Economics and Commerce, Guangdong University of Technology, Guangzhou 510520, China
4.
China Wealth (Asset) Management Registry & Custody Co. Ltd, Beijing 100045, China
5.
School of Mathematics, Shandong University, Jinan 250100, China

* Corresponding author: Yi Zhuang
* Corresponding author: Yi Zhuang

Received: January 31, 2017

Revised: January 31, 2018

Published: May 2019

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Abstract

In this article, we study a class of partially observed non-zero sum stochastic differential game based on forward and backward stochastic differential equations (FBSDEs). It is required that each player has his own observation equation, and the corresponding Nash equilibrium control is required to be adapted to the filtration generated by the observation process. To find the Nash equilibrium point, we establish the maximum principle as a necessary condition and derive the verification theorem as a sufficient condition. Applying the theoretical results and stochastic filtering theory, we obtain the explicit investment strategy of a partial information financial problem.

Keywords:

Forward-backward stochastic differential equation,
stochastic differential game,
maximum principle,
equilibrium point,
stochastic filtering.

Mathematics Subject Classification: Primary: 49N70; Secondary: 93C20, 93E11.

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