Singular Control in a Cash Management Model with Ambiguity

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

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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.

Date: 2023-09
New Economics Papers: this item is included in nep-upt
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