An Optimal Execution Problem with S-shaped Market Impact Functions

Takashi Kato

Papers from arXiv.org

Abstract: In this study, we extend the optimal execution problem with convex market impact function studied in Kato (2014) to the case where the market impact function is S-shaped, that is, concave on $[0, \bar {x}_0]$ and convex on $[\bar {x}_0, \infty )$ for some $\bar {x}_0 \geq 0$. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the optimal execution speed under the S-shaped market impact is equal to zero or larger than $\bar {x}_0$. Moreover, we provide some examples of the Black-Scholes model. We show that the optimal strategy for a risk-neutral trader with small shares is the time-weighted average price strategy whenever the market impact function is S-shaped.

Date: 2017-06, Revised 2017-10
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Published in Communications on Stochastic Analysis, Vol.11, No.3, pp.265-285 (2017)

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