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

In: 2012 Recent Advances in Financial Engineering Proceedings of the International Workshop on Finance 2012

Author

Listed:
  • Kensuke Ishitani
  • Takashi Kato

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.

Suggested Citation

  • Kensuke Ishitani & Takashi Kato, 2014. "Optimal Execution for Uncertain Market Impact: Derivation and Characterization of a Continuous-Time Value Function," World Scientific Book Chapters, in: Akihiko Takahashi & Yukio Muromachi & Takashi Shibata (ed.), 2012 Recent Advances in Financial Engineering Proceedings of the International Workshop on Finance 2012, chapter 5, pages 93-116, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814571647_0005
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