Adaptive Robust Control in Continuous-Time

28 Pages Posted: 5 May 2020 Last revised: 7 May 2020

See all articles by Theerawat Bhudisaksang

Theerawat Bhudisaksang

University of Oxford - Mathematical Institute

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: April 9, 2020

Abstract

We propose a continuous-time version of the adaptive robust methodology introduced in Bielecki et al. (2019). An agent solves a stochastic control problem where the underlying uncertainty follows a jump-diffusion process and the agent does not know the drift parameters of the process. The agent considers a set of alternative measures to make the control problem robust to model misspecification and employs a continuous-time estimator to learn the value of the unknown parameters to make the control problem adaptive to the arrival of new information. We use measurable selection theorems to prove the dynamic programming principle of the adaptive robust problem and show that the value function of the agent is characterised by a non-linear partial differential equation. As an example, we derive in closed-form the optimal adaptive robust strategy for an agent who acquires a large number of shares in an order-driven market and illustrates the financial performance of the execution strategy.

Keywords: adaptive robust control, model uncertainty, stochastic control, time-consistency, dynamic programming, optimal acquisition, online learning, algorithmic trading

Suggested Citation

Bhudisaksang, Theerawat and Cartea, Álvaro, Adaptive Robust Control in Continuous-Time (April 9, 2020). Available at SSRN: https://ssrn.com/abstract=3571991 or http://dx.doi.org/10.2139/ssrn.3571991

Theerawat Bhudisaksang (Contact Author)

University of Oxford - Mathematical Institute ( email )

Andrew Wiles Building
Radcliffe Observatory Quarter (550)
Oxford, OX2 6GG
United Kingdom

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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