# An Optimal Execution Problem with S-shaped Market Impact Functions

@article{Kato2017AnOE,
title={An Optimal Execution Problem with S-shaped Market Impact Functions},
author={Takashi Kato},
journal={arXiv: Mathematical Finance},
year={2017}
}
• Takashi Kato
• Published 2017
• Economics
• arXiv: Mathematical Finance
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… Expand
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