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A Pontryagin's Maximum Principle for Non-Zero Sum Differential Games of BSDEs with Applications
- 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.
- Subjects :
- Equilibrium point
Computer Science::Computer Science and Game Theory
Stochastic process
Differential equation
Computer Science Applications
Stochastic differential equation
Maximum principle
Zero-sum game
Control and Systems Engineering
Electrical and Electronic Engineering
Differential (infinitesimal)
Random variable
Mathematical economics
Mathematics
Subjects
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