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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, Tome 24 (2018) no. 2, pp. 639-676

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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.

DOI : 10.1051/cocv/2017042
Classification : 93E20, 60H30, 49L20, 49L25
Keywords: Second order Hamilton−Jacobi−Bellman equation, viscosity solution, infinite-horizon optimal control, stochastic differential equations with delays, existence and uniqueness

Zhou, Jianjun 1

1 
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     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},
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     zbl = {1401.93234},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017042/}
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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, Tome 24 (2018) no. 2, pp. 639-676. doi: 10.1051/cocv/2017042

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