In this paper, we investigate infinite horizon jump-diffusion forward-backward stochastic differential equations under some monotonicity conditions. We establish an existence and uniqueness theorem, two stability results and a comparison theorem for solutions to such kind of equations. Then the theoretical results are applied to study a kind of infinite horizon backward stochastic linear-quadratic optimal control problems, and then differential game problems. The unique optimal controls for the control problems and the unique Nash equilibrium points for the game problems are obtained in closed forms.
Accepté le :
DOI : 10.1051/cocv/2016055
Mots-clés : Forward-backward stochastic differential equation, monotonicity condition, stochastic optimal control, nonzero-sum stochastic differential game, linear-quadratic problem
@article{COCV_2017__23_4_1331_0,
author = {Yu, Zhiyong},
title = {Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1331--1359},
publisher = {EDP-Sciences},
volume = {23},
number = {4},
year = {2017},
doi = {10.1051/cocv/2016055},
mrnumber = {3716923},
zbl = {1375.60104},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2016055/}
}
TY - JOUR AU - Yu, Zhiyong TI - Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1331 EP - 1359 VL - 23 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2016055/ DO - 10.1051/cocv/2016055 LA - en ID - COCV_2017__23_4_1331_0 ER -
%0 Journal Article %A Yu, Zhiyong %T Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1331-1359 %V 23 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2016055/ %R 10.1051/cocv/2016055 %G en %F COCV_2017__23_4_1331_0
Yu, Zhiyong. Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1331-1359. doi : 10.1051/cocv/2016055. http://www.numdam.org/articles/10.1051/cocv/2016055/
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