Multi-asset Optimal Execution and Statistical Arbitrage Strategies under Ornstein--Uhlenbeck Dynamics

Philippe Bergault, Fayçal Drissi and Olivier Guéant
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Philippe Bergault: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Fayçal Drissi: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, University of Oxford

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Abstract: In recent years, academics, regulators, and market practitioners have increasingly addressed liquidity issues. Among the numerous problems addressed, the optimal execution of large orders is probably the one that has attracted the most research works, mainly in the case of single-asset portfolios. In practice, however, optimal execution problems often involve large portfolios comprising numerous assets, and models should consequently account for risks at the portfolio level. In this paper, we address multi-asset optimal execution in a model where prices have multivariate Ornstein--Uhlenbeck dynamics and where the agent maximizes the expected (exponential) utility of her Profit and Loss (PnL). We use the tools of stochastic optimal control and simplify the initial multidimensional Hamilton--Jacobi--Bellman equation into a system of ordinary differential equations (ODEs) involving a matrix Riccati ODE for which classical existence theorems do not apply. By using a priori estimates obtained thanks to optimal control tools, we nevertheless prove an existence and uniqueness result for the latter ODE and then deduce a verification theorem that provides a rigorous solution to the execution problem. Using examples based on data from the foreign exchange and stock markets, we eventually illustrate our results and discuss their implications for both optimal execution and statistical arbitrage.

Keywords: stochastic opti...; riccati equatio...; optimal executi...; statistical arb... (search for similar items in EconPapers)
Date: 2022-03
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Citations: View citations in EconPapers (7)

Published in SIAM Journal on Financial Mathematics, 2022, 13 (1), pp.353-390. ⟨10.1137/21M1407756⟩

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Working Paper: Multi-asset Optimal Execution and Statistical Arbitrage Strategies under Ornstein--Uhlenbeck Dynamics (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03680071

DOI: 10.1137/21M1407756

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