Differential games of partial information forward-backward doubly SDE and applications

Eddie C. M. Hui; Hua Xiao

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 1, page 78-94
  • ISSN: 1292-8119

Abstract

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This paper addresses a new differential game problem with forward-backward doubly stochastic differential equations. There are two distinguishing features. One is that our game systems are initial coupled, rather than terminal coupled. The other is that the admissible control is required to be adapted to a subset of the information generated by the underlying Brownian motions. We establish a necessary condition and a sufficient condition for an equilibrium point of nonzero-sum games and a saddle point of zero-sum games. To illustrate some possible applications, an example of linear-quadratic nonzero-sum differential games is worked out. Applying stochastic filtering techniques, we obtain an explicit expression of the equilibrium point.

How to cite

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Hui, Eddie C. M., and Xiao, Hua. "Differential games of partial information forward-backward doubly SDE and applications." ESAIM: Control, Optimisation and Calculus of Variations 20.1 (2014): 78-94. <http://eudml.org/doc/272892>.

@article{Hui2014,
abstract = {This paper addresses a new differential game problem with forward-backward doubly stochastic differential equations. There are two distinguishing features. One is that our game systems are initial coupled, rather than terminal coupled. The other is that the admissible control is required to be adapted to a subset of the information generated by the underlying Brownian motions. We establish a necessary condition and a sufficient condition for an equilibrium point of nonzero-sum games and a saddle point of zero-sum games. To illustrate some possible applications, an example of linear-quadratic nonzero-sum differential games is worked out. Applying stochastic filtering techniques, we obtain an explicit expression of the equilibrium point.},
author = {Hui, Eddie C. M., Xiao, Hua},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {stochastic differential game; partial information; forward-backward doubly stochastic differential equation; equilibrium point; stochastic filtering},
language = {eng},
number = {1},
pages = {78-94},
publisher = {EDP-Sciences},
title = {Differential games of partial information forward-backward doubly SDE and applications},
url = {http://eudml.org/doc/272892},
volume = {20},
year = {2014},
}

TY - JOUR
AU - Hui, Eddie C. M.
AU - Xiao, Hua
TI - Differential games of partial information forward-backward doubly SDE and applications
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2014
PB - EDP-Sciences
VL - 20
IS - 1
SP - 78
EP - 94
AB - This paper addresses a new differential game problem with forward-backward doubly stochastic differential equations. There are two distinguishing features. One is that our game systems are initial coupled, rather than terminal coupled. The other is that the admissible control is required to be adapted to a subset of the information generated by the underlying Brownian motions. We establish a necessary condition and a sufficient condition for an equilibrium point of nonzero-sum games and a saddle point of zero-sum games. To illustrate some possible applications, an example of linear-quadratic nonzero-sum differential games is worked out. Applying stochastic filtering techniques, we obtain an explicit expression of the equilibrium point.
LA - eng
KW - stochastic differential game; partial information; forward-backward doubly stochastic differential equation; equilibrium point; stochastic filtering
UR - http://eudml.org/doc/272892
ER -

References

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