OPTIMAL LIQUIDATION UNDER STOCHASTIC PRICE IMPACT

Weston Barger () and Matthew Lorig
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Weston Barger: Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
Matthew Lorig: Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 02, 1-28

Abstract: We assume a continuous-time price impact model similar to that of Almgren–Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop trading strategies for a trader who desires to liquidate his inventory but faces price impact as a result of his trading. For a fixed trading horizon, we perform coefficient expansion on the Hamilton–Jacobi–Bellman (HJB) equation associated with the trader’s value function. The coefficient expansion yields a sequence of partial differential equations that we solve to give closed-form approximations to the value function and optimal liquidation strategy. We examine some special cases of the optimal liquidation problem and give financial interpretations of the approximate liquidation strategies in these cases. Finally, we provide numerical examples to demonstrate the effectiveness of the approximations.

Keywords: Optimal execution; price impact; algorithmic trading; stochastic control; Hamilton–Jacobi–Bellman; asymptotics; coefficient expansion (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (13)

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DOI: 10.1142/S0219024918500590

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