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December 2020 Modelling information flows by Meyer-$\sigma $-fields in the singular stochastic control problem of irreversible investment
Peter Bank, David Besslich
Ann. Appl. Probab. 30(6): 2923-2962 (December 2020). DOI: 10.1214/20-AAP1577

Abstract

In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows when about the exogenous shocks and how and when she can act on this information. We propose to use Meyer-$\sigma $-fields as a flexible tool to model information flow in such situations. The possibilities of this approach are illustrated first in a very simple linear stochastic control problem and then in a fairly general formulation for the singular stochastic control problem of irreversible investment with inventory risk. For the latter, we illustrate in a first case study how different signals on exogenous jumps lead to different optimal controls, interpolating between the predictable and the optional case in a systematic manner.

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Peter Bank. David Besslich. "Modelling information flows by Meyer-$\sigma $-fields in the singular stochastic control problem of irreversible investment." Ann. Appl. Probab. 30 (6) 2923 - 2962, December 2020. https://doi.org/10.1214/20-AAP1577

Information

Received: 1 November 2018; Revised: 1 November 2019; Published: December 2020
First available in Project Euclid: 14 December 2020

Digital Object Identifier: 10.1214/20-AAP1577

Subjects:
Primary: 60H30, 91B70, 93E20

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 6 • December 2020
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