In this paper, we investigate a class of infinite-horizon optimal control problems for stochastic differential equations with delays for which the associated second order Hamilton−Jacobi−Bellman (HJB) equation is a nonlinear partial differential equation with delays. We propose a new concept for the viscosity solution including time t and identify the value function of the optimal control problems as a unique viscosity solution to the associated second order HJB equation.

Keywords: Second order Hamilton−Jacobi−Bellman equation, viscosity solution, infinite-horizon optimal control, stochastic differential equations with delays, existence and uniqueness

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@article{COCV_2018__24_2_639_0, author = {Zhou, Jianjun}, title = {A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated {HJB} equation}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {639--676}, publisher = {EDP-Sciences}, volume = {24}, number = {2}, year = {2018}, doi = {10.1051/cocv/2017042}, mrnumber = {3816408}, zbl = {1401.93234}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017042/} }

TY - JOUR AU - Zhou, Jianjun TI - A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 639 EP - 676 VL - 24 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017042/ DO - 10.1051/cocv/2017042 LA - en ID - COCV_2018__24_2_639_0 ER -

%0 Journal Article %A Zhou, Jianjun %T A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 639-676 %V 24 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017042/ %R 10.1051/cocv/2017042 %G en %F COCV_2018__24_2_639_0

Zhou, Jianjun. A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 2, pp. 639-676. doi : 10.1051/cocv/2017042. http://archive.numdam.org/articles/10.1051/cocv/2017042/

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