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Singular control in a cash management model with ambiguity

Author

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

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.

Suggested Citation

  • Archankul, Arnon & Ferrari, Giorgio & Hellmann, Tobias & Thijssen, Jacco J.J., 2025. "Singular control in a cash management model with ambiguity," European Journal of Operational Research, Elsevier, vol. 327(2), pages 500-514.
    • Handle: RePEc:eee:ejores:v:327:y:2025:i:2:p:500-514
    DOI: 10.1016/j.ejor.2025.07.023
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