Linear-quadratic stochastic delayed control and deep learning resolution

William Lefebvre () and Enzo Miller
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William Lefebvre: LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité, Global Markets - BNP-Paribas
Enzo Miller: LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité

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Abstract: We consider a class of stochastic control problems with a delayed control, both in drift and diffusion, of the type dX t = α t−d (bdt + σdW t). We provide a new characterization of the solution in terms of a set of Riccati partial differential equations. Existence and uniqueness are obtained under a sufficient condition expressed directly as a relation between the horizon T and the quantity d(b/σ) 2. Furthermore, a deep learning scheme is designed and used to illustrate the effect of delay on the Markowitz portfolio allocation problem with execution delay.

Keywords: Linear-quadratic stochastic control; delay; Riccati PDEs; Markowitz portfolio allocation (search for similar items in EconPapers)
Date: 2021-10
Note: View the original document on HAL open archive server: https://hal.science/hal-03145949v3
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Published in Journal of Optimization Theory and Applications, 2021, 191 (1), pp.134-168. ⟨10.1007/s10957-021-01923-x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03145949

DOI: 10.1007/s10957-021-01923-x

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