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.
Highlights
Cash is the most liquid asset and the most profitable
Xu and Zhu [16] studied the continuous and discrete time models of uncertain bang–bang control. These kinds of bang–bang control problems occupy an important position in optimal control theory
The results show that our model is a bang–bang control model, and managers only need to compare the future value of unit assets to make decisions about cash holding
Summary
Cash is the most liquid asset and the most profitable. A lack of cash affects the production and operation of an enterprise, and excess cash reduces the profit level of the enterprise. On the basis of uncertain differential equations, for uncertain continuous systems, Zhu [13] proposed an optimal control problem and established the expected value model of the problem. Xu and Zhu [16] studied the continuous and discrete time models of uncertain bang–bang control These kinds of bang–bang control problems occupy an important position in optimal control theory. Yan and Zhu [21] studied the uncertain switched systems bang–bang control model They gave the optimal equation of the model, and found the optimal solution to the problem using a two-stage algorithm. The results show that our model is a bang–bang control model, and managers only need to compare the future value of unit assets to make decisions about cash holding. The last section presents our conclusions and the limitations of the paper
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