MODELLING INFORMATION FLOWS BY MEYER-σ-FIELDS IN THE SINGULAR STOCHASTIC CONTROL PROBLEM OF IRREVERSIBLE INVESTMENT

• 成果类型: Article
• 署名作者: Bank, Peter; Besslich, David
• 署名单位: Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1577
• 发表日期: 2020
• 页码: 2923-2962
• 关键词: optimal stopping time; optimization; BOUNDARY; THEOREM

摘要

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.