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.
Mots clés : stochastic differential game, partial information, forward-backward doubly stochastic differential equation, equilibrium point, stochastic filtering
@article{COCV_2014__20_1_78_0,
author = {Hui, Eddie C. M. and Xiao, Hua},
title = {Differential games of partial information forward-backward doubly {SDE} and applications},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {78--94},
publisher = {EDP-Sciences},
volume = {20},
number = {1},
year = {2014},
doi = {10.1051/cocv/2013055},
mrnumber = {3182691},
zbl = {1286.49043},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2013055/}
}
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 SP - 78 EP - 94 VL - 20 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2013055/ DO - 10.1051/cocv/2013055 LA - en ID - COCV_2014__20_1_78_0 ER -
%0 Journal Article %A Hui, Eddie C. M. %A Xiao, Hua %T Differential games of partial information forward-backward doubly SDE and applications %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 78-94 %V 20 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2013055/ %R 10.1051/cocv/2013055 %G en %F COCV_2014__20_1_78_0
Hui, Eddie C. M.; Xiao, Hua. Differential games of partial information forward-backward doubly SDE and applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 1, pp. 78-94. doi : 10.1051/cocv/2013055. http://www.numdam.org/articles/10.1051/cocv/2013055/
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