The paper is concerned with optimal control of a stochastic differential system reflected in a domain. The cost functional is implicitly defined via a generalized backward stochastic differential equation developed by Pardoux and Zhang [Probab. Theory Relat. Fields 110 (1998) 535–558]. The value function is shown to be the unique viscosity solution to the associated Hamilton–Jacobi–Bellman equation, which is a fully nonlinear parabolic partial differential equation with a nonlinear Neumann boundary condition. The proof requires new estimates for the reflected stochastic differential system.
DOI : 10.1051/cocv/2014062
Mots-clés : Hamilton–Jacobi–Bellman equation, nonlinear Neumann boundary, value function, backward stochastic differential equations, dynamic programming principle, viscosity solution
@article{COCV_2015__21_4_1150_0,
author = {Li, Juan and Tang, Shanjian},
title = {Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1150--1177},
publisher = {EDP-Sciences},
volume = {21},
number = {4},
year = {2015},
doi = {10.1051/cocv/2014062},
mrnumber = {3395759},
zbl = {1341.49020},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2014062/}
}
TY - JOUR AU - Li, Juan AU - Tang, Shanjian TI - Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 1150 EP - 1177 VL - 21 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014062/ DO - 10.1051/cocv/2014062 LA - en ID - COCV_2015__21_4_1150_0 ER -
%0 Journal Article %A Li, Juan %A Tang, Shanjian %T Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 1150-1177 %V 21 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014062/ %R 10.1051/cocv/2014062 %G en %F COCV_2015__21_4_1150_0
Li, Juan; Tang, Shanjian. Optimal stochastic control with recursive cost functionals of stochastic differential systems reflected in a domain. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1150-1177. doi : 10.1051/cocv/2014062. http://www.numdam.org/articles/10.1051/cocv/2014062/
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