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Singular Control in a Cash Management Model with Ambiguity

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

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 numerically 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.

Suggested Citation

  • Arnon Archankul & Giorgio Ferrari & Tobias Hellmann & Jacco J. J. Thijssen, 2023. "Singular Control in a Cash Management Model with Ambiguity," Papers 2309.12014, arXiv.org.
    • Handle: RePEc:arx:papers:2309.12014
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    References listed on IDEAS

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