Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/305822 
Erscheinungsjahr: 
2023
Quellenangabe: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 27 [Issue:] 3 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2023 [Pages:] 713-768
Verlag: 
Springer, Berlin, Heidelberg
Zusammenfassung: 
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 btriggers the investor's optimal selling rule. The curve  bis 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.
Schlagwörter: 
Optimal execution problem
Multiplicative price impact
Singular stochastic control
Partial observation
Optimal stopping
JEL: 
G11
C61
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Dokumentart: 
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Dokumentversion: 
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