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

Communications on Stochastic Analysis, 9(3), 343-366 (2015)

24 Pages Posted: 9 Jun 2015 Last revised: 8 Nov 2015

See all articles by Kensuke Ishitani

Kensuke Ishitani

Tokyo Metropolitan University

Takashi Kato

Association of Mathematical Finance Laboratory (AMFiL)

Date Written: March 10, 2015

Abstract

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 of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton--Jacobi--Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.

Keywords: Optimal execution, market impact, liquidity uncertainty, Levy process

Suggested Citation

Ishitani, Kensuke and Kato, Takashi, Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact (March 10, 2015). Communications on Stochastic Analysis, 9(3), 343-366 (2015), Available at SSRN: https://ssrn.com/abstract=2616120 or http://dx.doi.org/10.2139/ssrn.2616120

Kensuke Ishitani

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 (Contact Author)

Association of Mathematical Finance Laboratory (AMFiL) ( email )

2-10
Kojimachi
Chiyoda, Tokyo 102-0083
Japan

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