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.
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://www.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://www.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://www.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://www.numdam.org/articles/10.1051/cocv/2013051/
[1] , and , Some recent aspects of differential game theory. Dynamic Games Appl. 1 (2011) 74-114 | MR | Zbl
[2] , and , Nash equilibrium payoffs for nonzero-sum Stochastic differential games. SIAM J. Control Optim. 43 (2004) 624-642. | MR | Zbl
[3] and , Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations. arXiv:math/0702131. | MR | Zbl
[4] and , Stochastic differential games with reflection and related obstacle problems for Isaacs equations arXiv:0707.1133. | MR | Zbl
[5] , , , and , Reflected solutions of backward SDE's, and related obstacle problems for PDE's. Ann. Probab. 25 (1997) 702-737. | MR | Zbl
[6] , and , Backward stochastic differential equation in finance. Math. Finance 7 (1997) 1-71. | MR | Zbl
[7] , , On the existence of value functions of twoplayer, zero-sum stochastic differential games. Indiana Univ. Math. J. 38 (1989) 293-314. | MR | Zbl
[8] , and , 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] , 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] , Nash equilibrium payoffs for stochastic differential games with jumps and coupled nonlinear cost functionals. arXiv:1108.3695v1.
[11] , 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] and , Dynamic programming principle for one kind of stochastic recursive optimal control problem and Hamilton-Jacobi-Bellman equation. arXiv:0704.3775. | MR
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