An optimal execution problem in the volume-dependent Almgren–Chriss model

Article type: Research Article

Authors: Kato, Takashi^{; *}

Affiliations: Association of Mathematical Finance Laboratory (AMFiL), Chiyoda, Tokyo, Japan

Correspondence: [*] Corresponding author: Takashi Kato, Association of Mathematical Finance Laboratory (AMFiL), 2–10 Kojimachi, Chiyoda, Tokyo 102-0083, Japan. E-mail: takashi.kato@mathfi-lab.com.

Abstract: In this study, we introduce an explicit trading-volume process into the Almgren–Chriss model, which is a standard model for optimal execution. We propose a penalization method for deriving a verification theorem for an adaptive optimization problem. We also discuss the optimality of the volume-weighted average-price strategy of a risk-neutral trader. Moreover, we derive a second-order asymptotic expansion of the optimal strategy and verify its accuracy numerically.

Keywords: Optimal execution problem, market trading volume, volume-weighted average price (VWAP), market impact

DOI: 10.3233/AF-170198

Journal: Algorithmic Finance, vol. 7, no. 1-2, pp. 1-14, 2018