The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the unique viscosity solution of the related Hamilton−Jacobi−Bellman−Isaacs (HJBI) equation.

Accepted:

DOI: 10.1051/cocv/2017044

Keywords: G-Brownian motion, backward stochastic differential equations, stochastic optimal control, dynamic programming principle

^{1}; Wang, Falei

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@article{COCV_2018__24_2_873_0, author = {Hu, Mingshang and Wang, Falei}, title = {Stochastic optimal control problem with infinite horizon driven by {G-Brownian} motion}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {873--899}, publisher = {EDP-Sciences}, volume = {24}, number = {2}, year = {2018}, doi = {10.1051/cocv/2017044}, mrnumber = {3816420}, zbl = {1401.93224}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017044/} }

TY - JOUR AU - Hu, Mingshang AU - Wang, Falei TI - Stochastic optimal control problem with infinite horizon driven by G-Brownian motion JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 873 EP - 899 VL - 24 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017044/ DO - 10.1051/cocv/2017044 LA - en ID - COCV_2018__24_2_873_0 ER -

%0 Journal Article %A Hu, Mingshang %A Wang, Falei %T Stochastic optimal control problem with infinite horizon driven by G-Brownian motion %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 873-899 %V 24 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017044/ %R 10.1051/cocv/2017044 %G en %F COCV_2018__24_2_873_0

Hu, Mingshang; Wang, Falei. Stochastic optimal control problem with infinite horizon driven by G-Brownian motion. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 2, pp. 873-899. doi : 10.1051/cocv/2017044. http://archive.numdam.org/articles/10.1051/cocv/2017044/

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