# 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} }

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

#### 2 Citations

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

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- Algorithmic Finance
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