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Nash equilibrium payoffs for stochastic differential games with reflection

Published online by Cambridge University Press:  27 August 2013

Qian Lin
Qian Lin*
Affiliation:
Center for Mathematical Economics, Bielefeld University, Postfach 100131, 33501 Bielefeld, Germany. linqian1824@163.com
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Abstract

In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations.

Keywords

Backward stochastic differential equationsdynamic programming principleNash equilibrium payoffsstochastic differential games
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 4 , October 2013 , pp. 1189 - 1208
Copyright
© EDP Sciences, SMAI, 2013

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References

Buckdahn, R., Cardaliaguet, P. and Quincampoix, M., Some recent aspects of differential game theory. Dynamic Games Appl. 1 (2011) 74–114 Google Scholar
Buckdahn, R., Cardaliaguet, P. and Rainer, C., Nash equilibrium payoffs for nonzero-sum Stochastic differential games. SIAM J. Control Optim. 43 (2004) 624–642. Google Scholar
R. Buckdahn and J. Li, Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations. arXiv:math/0702131.
R. Buckdahn and J. Li, Stochastic differential games with reflection and related obstacle problems for Isaacs equations arXiv:0707.1133.
El Karoui, N., Kapoudjian, C., Pardoux, E., Peng, S. and Quenez, M.C., Reflected solutions of backward SDE’s, and related obstacle problems for PDE’s. Ann. Probab. 25 (1997) 702–737. Google Scholar
El Karoui, N., Peng, S. and Quenez, M.C., Backward stochastic differential equation in finance. Math. Finance 7 (1997) 1–71. Google Scholar
Fleming, W.H., Souganidis, P.E., On the existence of value functions of twoplayer, zero-sum stochastic differential games. Indiana Univ. Math. J. 38 (1989) 293–314. Google Scholar
S. Hamadène, J. Lepeltier and A. Matoussi, Double barrier backward SDEs with continuous coefficient. In Backward Stochastic Differential Equations. Pitman Res. Notes Math. Ser., vol. 364. Edited by El Karoui Mazliak (1997) 161–175.
Lin, Q., A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals. Stochastic Process. Appl. 122 (2012) 357–385. Google Scholar
Q. Lin, Nash equilibrium payoffs for stochastic differential games with jumps and coupled nonlinear cost functionals. arXiv:1108.3695v1.
S. Peng, Backward stochastic differential equations–stochastic optimization theory and viscosity solutions of HJB equations, in Topics Stoch. Anal., edited by J. Yan, S. Peng, S. Fang and L. Wu., Ch. 2 (Chinese vers.) (1997).
Z. Wu and Z. Yu, Dynamic programming principle for one kind of stochastic recursive optimal control problem and Hamilton-Jacobi-Bellman equation. arXiv:0704.3775.