|Publication ahead of print|
|Published online||26 January 2018|
A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation∗
College of Science, Northwest A&F University, Yangling 712100, Shaanxi, P.R. China.
Corresponding author: email@example.com
Received: 17 March 2016
Revised: 22 April 2017
Accepted: 6 June 2017
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.
Mathematics Subject Classification: 93E20 / 60H30 / 49L20 / 49L25
Key words: Second order Hamilton−Jacobi−Bellman equation / viscosity solution / infinite-horizon optimal control / stochastic differential equations with delays / existence and uniqueness
© EDP Sciences, SMAI 2018
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