Issue |
ESAIM: COCV
Volume 24, Number 2, April–June 2018
|
|
---|---|---|
Page(s) | 639 - 676 | |
DOI | https://doi.org/10.1051/cocv/2017042 | |
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
a Corresponding author: zhoujj198310@163.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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