Stochastic Optimal Control with Delay in the Control I: Solving the HJB Equation through Partial Smoothing

DOI10.1137/16M1070128zbMath1375.93140arXiv1607.06502OpenAlexW2952441701MaRDI QIDQ5358870

Federica Masiero, Fausto Gozzi

Publication date: 22 September 2017

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.06502

zbMATH Keywords

second order Hamilton-Jacobi-Bellman equations in infinite dimensiondelay in the controllack of structure conditionoptimal control of stochastic delay equationssmoothing properties of transition semigroups

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Markov semigroups and applications to diffusion processes (47D07) Optimal stochastic control (93E20) Stochastic integral equations (60H20) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (18)

Pairs trading under delayed cointegration ⋮ Stochastic Control Problems with Unbounded Control Operators: Solutions Through Generalized Derivatives ⋮ Anticipated mean-field backward stochastic differential equations with jumps ⋮ A notion of viscosity solutions to second-order Hamilton–Jacobi–Bellman equations with delays ⋮ Systemic risk and stochastic games with delay ⋮ Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula ⋮ Partial smoothing of delay transition semigroups acting on special functions ⋮ Linear-Quadratic Mean Field Stackelberg Games with State and Control Delays ⋮ Stochastic Optimal Control with Delay in the Control II: Verification Theorem and Optimal Feedbacks ⋮ Optimal control of path-dependent McKean-Vlasov SDEs in infinite-dimension ⋮ Stochastic Control with Delayed Information and Related Nonlinear Master Equation ⋮ Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost ⋮ Semilinear Kolmogorov equations on the space of continuous functions via BSDEs ⋮ Delay optimal control and viscosity solutions to associated Hamilton–Jacobi–Bellman equations ⋮ Infinite horizon stochastic maximum principle for stochastic delay evolution equations in Hilbert spaces ⋮ Recurrent neural networks for stochastic control problems with delay ⋮ Errata: Stochastic Optimal Control with Delay in the Control I: Solving the HJB Equation through Partial Smoothing, and Stochastic Optimal Control with Delay in the Control II: Verification Theorem and Optimal Feedbacks ⋮ On the relation between the Girsanov transform and the Kolmogorov equations for SPDEs

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