An optimal execution problem with market impact
type: Item
instance of: scholarly article
title: An optimal execution problem with market impact
zbMATH Open document ID: 1403.91344
author: Takashi Kato
published in: Finance and Stochastics
publication date: 2014-09-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/0907.3282
review text: The paper deals with the optimal execution problem when an impact of a continuous-time market model is considered. The problem is formulated as a stochastic control problem where properties of the corresponding value function are investigated. First one studies the continuity of the value function: the obtained results e.g. show that an instantaneous liquidation of large volume makes no sense when the market impact for large trade is strong. Further one shows the validity of Bellman principle (i.e. the semigroup property) so that the value function can be characterised as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. Finally, a case is considered where the trader needs to liquidate all holdings of the security: it is shown that such a liquidation does not influence the form of the corresponding value function.
reviewed by: Tomáš Cipra
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 91G80
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 49L25
zbMATH DE Number: 6348477
zbMATH Keywords: optimal execution
zbMATH Keywords: market impact
zbMATH Keywords: liquidity problems
zbMATH Keywords: Hamilton-Jacobi-Bellman equation
zbMATH Keywords: viscosity solutions
MaRDI profile type: Publication
OpenAlex ID: W3121867036
arXiv ID: 0907.3282
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DOI: 10.1007/S00780-014-0232-0
description: scientific article; zbMATH DE number 6348477