๐ค AI Summary
This paper investigates the singular control problem of corporate cash reserves under ambiguity, focusing on how managerial maxmin preferences shape optimal cash policies. Methodologically, it constructs a worst-case model based on a ฮบ-ignorance prior set andโnoveltyโthe first integration of maxmin preferences into a singular control framework, yielding a robust barrier policy under ambiguity. Using diffusion modeling, verification theorem analysis, and numerical simulations, the study demonstrates that heightened ambiguity substantially increases worst-case control costs and narrows the no-intervention region, thereby exerting a structural impact on cash holding behavior. The contribution lies in providing both a new theoretical lens for understanding corporate cash management under Knightian uncertainty and actionable, ambiguity-robust cash policy guidelines grounded in rigorous stochastic control theory.
๐ 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.
