Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact
Trading and Market Microstructure
2015-06-23 v6 Probability
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.
Keywords
Cite
@article{arxiv.1301.6485,
title = {Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact},
author = {Kensuke Ishitani and Takashi Kato},
journal= {arXiv preprint arXiv:1301.6485},
year = {2015}
}
Comments
17 pages. Forthcoming in "Communications on Stochastic Analysis."