2021/03/25 by Philippe Bergault, Bergault, Philippe, Fayçal Drissi +3 · 2 citations
Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #Financial Markets and Investment Strategies #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR) #q-fin.TR
paper · pdf · doi:10.48550/arxiv.2103.13773
openalex publication_date 2021/03/25 · arxiv created 2022/03/22 · arxiv updated 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent years, academics, regulators, and market practitioners have increasingly addressed liquidity issues. Amongst 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 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.