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

See all articles by Kensuke Ishitani

Kensuke Ishitani

Tokyo Metropolitan University

Takashi Kato

Association of Mathematical Finance Laboratory (AMFiL)

Date Written: January 29, 2013

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: optimal execution, market impact, liquidity uncertainty, Levy process

JEL Classification: G11, G33

Suggested Citation

Ishitani, Kensuke and Kato, Takashi, Mathematical Formulation of an Optimal Execution Problem with Uncertain Market Impact (January 29, 2013). Communications on Stochastic Analysis, 9(1), 113-129 (2015)., Available at SSRN: https://ssrn.com/abstract=2208306 or http://dx.doi.org/10.2139/ssrn.2208306

Kensuke Ishitani (Contact Author)

Tokyo Metropolitan University ( email )

1-1 Minami-Osawa, Hachioji-shi
Tokyo, 192-0397
Japan
+81-42-677-2473 (Phone)

HOME PAGE: http://www.tmu.ac.jp/stafflist/data/a/12748.html

Takashi Kato

Association of Mathematical Finance Laboratory (AMFiL) ( email )

2-10
Kojimachi
Chiyoda, Tokyo 102-0083
Japan

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