Optimal Uncertain Controls for Cash Holding Problems

Abstract

Determining whether an enterprise has target holdings and figuring out how to reasonably determine these cash holdings are common problems faced by all enterprises. This paper first establishes an uncertain optimal cash holdings model with a security area constraint, and then proves that the model is a typical bang–bang control model. The control variables in the model can be expressed as a symbolic function. Then, under the specific objective function, the optimal cash holdings are discussedfor two casesincluding whether to consider transaction costs or not. Finally, the applicability of the model is verified by specific examples, and the influences of factors, including risky asset returns and the transaction cost of unit securities on decision-making results are discussed.