Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact
Communications on Stochastic Analysis, 9(1), 113-129 (2015).
17 Pages Posted: 31 Jan 2013 Last revised: 22 Jun 2015
Date Written: January 29, 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 problem with a Levy process.
Keywords: optimal execution, market impact, liquidity uncertainty, Levy process
JEL Classification: G11, G33
Suggested Citation: Suggested Citation