Singular control in a cash management model with ambiguity

Arnon Archankul, Giorgio Ferrari, Tobias Hellmann and Jacco J.J. Thijssen

European Journal of Operational Research, 2025, vol. 327, issue 2, 500-514

Abstract: We consider a singular control model of cash reserve management, driven by a diffusion under ambiguity. The manager is assumed to have maxmin preferences over a set of priors characterized by κ-ignorance. A verification theorem is established to determine the firm’s cost function and the optimal cash policy; the latter taking the form of a control barrier policy. In a model driven by arithmetic Brownian motion, we use Dynkin games to show that an increase in ambiguity leads to higher expected costs under the worst-case prior and a narrower inaction region. The latter effect can be used to provide an ambiguity-driven explanation for observed cash management behavior. Our findings can be applied to broader applications of singular control in managing inventories under ambiguity.

Keywords: Singular control; Ambiguity; Inventory models (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:327:y:2025:i:2:p:500-514

DOI: 10.1016/j.ejor.2025.07.023

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