# Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact

@article{Ishitani2013MathematicalFO, title={Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact}, author={Kensuke Ishitani and Takashi Kato}, journal={ERN: Optimization Techniques; Programming Models; Dynamic Analysis (Topic)}, year={2013} }

We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a deterministic part increasing with execution volume and a positive stochastic noise part. Then, we derive a continuous-time model as a limit of a discrete-time value function. We find that the continuous-time value function is characterized by a stochastic control… Expand

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#### 3 Citations

An Optimal Execution Problem with S-shaped Market Impact Functions

- Economics
- 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,… Expand

An Optimal Execution Problem with S-Shaped Market Impact Functions

- Mathematics, Economics
- 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,… Expand

Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

- Economics, Mathematics
- 2015

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit… Expand

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