Optimal execution with multiplicative price impact and incomplete information on the return

Felix Dammann () and Giorgio Ferrari ()
Additional contact information
Felix Dammann: Bielefeld University
Giorgio Ferrari: Bielefeld University

Finance and Stochastics, 2023, vol. 27, issue 3, No 4, 713-768

Abstract: Abstract We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time horizon a fixed amount of assets in order to maximise a net expected profit functional, and lump-sum as well as singularly continuous actions are allowed. Our mathematical modelling leads to a singular stochastic control problem featuring a finite-fuel constraint and partial observation. We provide a complete analysis of an equivalent three-dimensional degenerate problem under full information, whose state process is composed of the asset price dynamics, the amount of available assets in the portfolio, and the investor’s belief about the true value of the asset’s trend. Its value function and optimal execution rule are expressed in terms of the solution to a truly two-dimensional optimal stopping problem, whose associated belief-dependent free boundary b $b$ triggers the investor’s optimal selling rule. The curve b $b$ is uniquely determined through a nonlinear integral equation, for which we derive a numerical solution through an application of the Monte Carlo method. This allows us to understand the value of information in our model as well as the sensitivity of the problem’s solution with respect to the relevant model parameters.

Keywords: Optimal execution problem; Multiplicative price impact; Singular stochastic control; Partial observation; Optimal stopping; 93E20; 93C41; 49L20; 91G80 (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00780-023-00508-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:finsto:v:27:y:2023:i:3:d:10.1007_s00780-023-00508-y

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-023-00508-y

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().