Nash equilibrium payoffs for stochastic differential games with reflection
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1189-1208.

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.

DOI : 10.1051/cocv/2013051
Classification : 49L25, 60H10, 60H30, 90C39
Mots clés : backward stochastic differential equations, dynamic programming principle, Nash equilibrium payoffs, stochastic differential games
@article{COCV_2013__19_4_1189_0,
     author = {Lin, Qian},
     title = {Nash equilibrium payoffs for stochastic differential games with reflection},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1189--1208},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {4},
     year = {2013},
     doi = {10.1051/cocv/2013051},
     mrnumber = {3182685},
     zbl = {1283.49043},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv/2013051/}
}
TY  - JOUR
AU  - Lin, Qian
TI  - Nash equilibrium payoffs for stochastic differential games with reflection
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2013
SP  - 1189
EP  - 1208
VL  - 19
IS  - 4
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/cocv/2013051/
DO  - 10.1051/cocv/2013051
LA  - en
ID  - COCV_2013__19_4_1189_0
ER  - 
%0 Journal Article
%A Lin, Qian
%T Nash equilibrium payoffs for stochastic differential games with reflection
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2013
%P 1189-1208
%V 19
%N 4
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/cocv/2013051/
%R 10.1051/cocv/2013051
%G en
%F COCV_2013__19_4_1189_0
Lin, Qian. Nash equilibrium payoffs for stochastic differential games with reflection. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1189-1208. doi : 10.1051/cocv/2013051. http://archive.numdam.org/articles/10.1051/cocv/2013051/

[1] R. Buckdahn, P. Cardaliaguet and M. Quincampoix, Some recent aspects of differential game theory. Dynamic Games Appl. 1 (2011) 74-114 | MR | Zbl

[2] R. Buckdahn, P. Cardaliaguet and C. Rainer, Nash equilibrium payoffs for nonzero-sum Stochastic differential games. SIAM J. Control Optim. 43 (2004) 624-642. | MR | Zbl

[3] R. Buckdahn and J. Li, Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations. arXiv:math/0702131. | MR | Zbl

[4] R. Buckdahn and J. Li, Stochastic differential games with reflection and related obstacle problems for Isaacs equations arXiv:0707.1133. | MR | Zbl

[5] N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng and M.C. Quenez, Reflected solutions of backward SDE's, and related obstacle problems for PDE's. Ann. Probab. 25 (1997) 702-737. | MR | Zbl

[6] N. El Karoui, S. Peng and M.C. Quenez, Backward stochastic differential equation in finance. Math. Finance 7 (1997) 1-71. | MR | Zbl

[7] W.H. Fleming, P.E. Souganidis, On the existence of value functions of twoplayer, zero-sum stochastic differential games. Indiana Univ. Math. J. 38 (1989) 293-314. | MR | Zbl

[8] 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. | MR | Zbl

[9] Q. Lin, A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals. Stochastic Process. Appl. 122 (2012) 357-385. | MR | Zbl

[10] Q. Lin, Nash equilibrium payoffs for stochastic differential games with jumps and coupled nonlinear cost functionals. arXiv:1108.3695v1.

[11] 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).

[12] 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. | MR

Cité par Sources :