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arXiv · 1301.6485

Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact

Kensuke Ishitani·Takashi Kato
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Abstract

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 problem with a Levy process.

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Kensuke Ishitani, Takashi Kato. 2013-01-28. Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact. https://arxiv.org/abs/1301.6485

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