Nash equilibrium payoffs for stochastic differential games with reflection

Qian Lin

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 4, page 1189-1208
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Lin, Qian. "Nash equilibrium payoffs for stochastic differential games with reflection." ESAIM: Control, Optimisation and Calculus of Variations 19.4 (2013): 1189-1208. <http://eudml.org/doc/272904>.

@article{Lin2013,
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.},
author = {Lin, Qian},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {backward stochastic differential equations; dynamic programming principle; Nash equilibrium payoffs; stochastic differential games},
language = {eng},
number = {4},
pages = {1189-1208},
publisher = {EDP-Sciences},
title = {Nash equilibrium payoffs for stochastic differential games with reflection},
url = {http://eudml.org/doc/272904},
volume = {19},
year = {2013},
}

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
PB - EDP-Sciences
VL - 19
IS - 4
SP - 1189
EP - 1208
AB - 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.
LA - eng
KW - backward stochastic differential equations; dynamic programming principle; Nash equilibrium payoffs; stochastic differential games
UR - http://eudml.org/doc/272904
ER -

References

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  9. [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. Zbl1237.60047MR2860453
  10. [10] Q. Lin, Nash equilibrium payoffs for stochastic differential games with jumps and coupled nonlinear cost functionals. arXiv:1108.3695v1. Zbl1333.60124
  11. [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. [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. Zbl1171.49022MR2452889

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