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A Pontryagin's Maximum Principle for Non-Zero Sum Differential Games of BSDEs with Applications

Authors :
Zhiyong Yu
Guangchen Wang
Source :
IEEE Transactions on Automatic Control. 55:1742-1747
Publication Year :
2010
Publisher :
Institute of Electrical and Electronics Engineers (IEEE), 2010.

Abstract

This technical note is concerned with a maximum principle for a new class of non-zero sum stochastic differential games. The most distinguishing feature, compared with the existing literature, is that the game systems are described by backward stochastic differential equations (BSDEs). This kind of games are motivated by some interesting phenomena arising from financial markets and can be used to characterize the players with different levels of utilities. We establish a necessary condition and a sufficient condition in the form of maximum principle for open-loop equilibrium point of the foregoing games respectively. To explain the theoretical results, we use them to study a financial problem.

Details

ISSN :
15582523 and 00189286
Volume :
55
Database :
OpenAIRE
Journal :
IEEE Transactions on Automatic Control
Accession number :
edsair.doi...........f73f99e7970506119a82081e7b47da8f
Full Text :
https://doi.org/10.1109/tac.2010.2048052