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Linear-quadratic stochastic delayed control and deep learning resolution

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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)

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.

Suggested Citation

  • William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Post-Print hal-03145949, HAL.
    • Handle: RePEc:hal:journl:hal-03145949
    DOI: 10.1007/s10957-021-01923-x
    Note: View the original document on HAL open archive server: https://hal.science/hal-03145949v3
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    References listed on IDEAS

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