Singular Control in a Cash Management Model with Ambiguity

Arnon Archankul, Giorgio Ferrari, Tobias Hellmann and Jacco J.J. Thijssen
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Arnon Archankul: Center for Mathematical Economics, Bielefeld University
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Tobias Hellmann: Center for Mathematical Economics, Bielefeld University
Jacco J.J. Thijssen: Center for Mathematical Economics, Bielefeld University

No 731, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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 $\kappa$-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)
Pages: 33
Date: 2025-08-14
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:731

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