Linear-Quadratic Stochastic Delayed Control and Deep Learning Resolution

William Lefebvre () and Enzo Miller ()
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William Lefebvre: BNP Paribas Global Markets
Enzo Miller: Université de Paris and Sorbonne Université

Journal of Optimization Theory and Applications, 2021, vol. 191, issue 1, No 6, 134-168

Abstract: Abstract We consider a simple class of stochastic control problems with a delayed control, in both the drift and the diffusion part of the state stochastic differential equation. We provide a new characterization of the solution in terms of a set of Riccati partial differential equations. Existence and uniqueness of a solution are obtained under a sufficient condition expressed directly as a relation between the time horizon, the drift, the volatility and the delay. Furthermore, a deep learning scheme (The code is available in a IPython notebook .) is designed and used to illustrate the effect of the delay feature on the Markowitz portfolio allocation problem with execution delay.

Keywords: Linear-quadratic stochastic control; Delay; Riccati PDEs; Markowitz portfolio allocation; Deep learning; 93E20; 60H10; 34K50 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-021-01923-x

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