The optimal cash holding models for stochastic cash management of continuous time

In business, enterprises need to maintain stable cash flows to meet the demands for payments in order to reduce the probability of possible bankruptcy. In this paper, we propose the optimal cash holding models in terms of continuous time and managers' risk preference in the framework of stochastic control theory in the setting of cash balance accounting with the interval of a safe area for cash holdings. Formulas for the optimal cash holdings are analytically derived with a widely used family of power utility functions. Our models can be seen as an extension of Miller-Orr model to solve the cash holding problem of continuous time from the accounting perspective. Numerical examples are also provided to illustrate the feasibility of the developed optimal cashing holding models of continuous time.