Optimal Execution for Uncertain Market Impact: Derivation and Characterization of a Continuous-Time Value Function

Kensuke Ishitani and Takashi Kato

Chapter 5 in Recent Advances in Financial Engineering 2012:Proceedings of the International Workshop on Finance 2012, 2014, pp 93-116 from World Scientific Publishing Co. Pte. Ltd.

Abstract: In this paper, we study an optimal execution problem in the case of uncertainty in market impact to derive a more realistic market model. Our model is a generalized version of that in [6], where a model of optimal execution with deterministic market impact was formulated. First, we construct a discrete-time model as a value function of an optimal execution problem. We express the market impact function as a product of a deterministic part (an increasing function with respect to the trader's execution volume) and a noise part (a positive random variable). 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 an optimal control problem with a Lévy process and investigate some of its properties, which are mathematical generalizations of the results in [6]. We also consider a typical example of the execution problem for a risk-neutral trader under log-linear/quadratic market impact with Gamma-distributed noise.

Keywords: Financial Engineering; Mathematical Finance; Money & Banking; Risk Management; Real Option; Corporate Finance; Computational Finance (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789814571647_0005 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789814571647_0005 (text/html)
Ebook Access is available upon purchase.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:wschap:9789814571647_0005

Ordering information: This item can be ordered from

Access Statistics for this chapter

More chapters in World Scientific Book Chapters from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().