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

Dammann F, Ferrari G (2023)
Finance and Stochastics 27: 713–768.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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 max-imise a net expected profit functional, and lump-sum as well as singularly continuous actions are allowed. Our mathematical modelling leads to a singular stochastic con-trol 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 asso-ciated belief-dependent free boundary b triggers the investor's optimal selling rule. The curve 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.
Stichworte
Optimal execution problem; Multiplicative price impact; Singular; stochastic control; Partial observation; Optimal stopping
Erscheinungsjahr
2023
Zeitschriftentitel
Finance and Stochastics
Band
27
Seite(n)
713–768
ISSN
0949-2984
eISSN
1432-1122
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2981371

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Dammann F, Ferrari G. Optimal execution with multiplicative price impact and incomplete information on the return. Finance and Stochastics . 2023;27: 713–768.
Dammann, F., & Ferrari, G. (2023). Optimal execution with multiplicative price impact and incomplete information on the return. Finance and Stochastics , 27, 713–768. https://doi.org/10.1007/s00780-023-00508-y
Dammann, Felix, and Ferrari, Giorgio. 2023. “Optimal execution with multiplicative price impact and incomplete information on the return”. Finance and Stochastics 27: 713–768.
Dammann, F., and Ferrari, G. (2023). Optimal execution with multiplicative price impact and incomplete information on the return. Finance and Stochastics 27, 713–768.
Dammann, F., & Ferrari, G., 2023. Optimal execution with multiplicative price impact and incomplete information on the return. Finance and Stochastics , 27, p 713–768.
F. Dammann and G. Ferrari, “Optimal execution with multiplicative price impact and incomplete information on the return”, Finance and Stochastics , vol. 27, 2023, pp. 713–768.
Dammann, F., Ferrari, G.: Optimal execution with multiplicative price impact and incomplete information on the return. Finance and Stochastics . 27, 713–768 (2023).
Dammann, Felix, and Ferrari, Giorgio. “Optimal execution with multiplicative price impact and incomplete information on the return”. Finance and Stochastics 27 (2023): 713–768.
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2024-07-02T13:46:52Z
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