Fall 12-2021

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Finance

Kenneth Yung

David Selover

#### Abstract

For any individual person or firm, there is a trade-off between carrying too much or too little cash on hand to meet the day-to-day transactions demand for cash. The BAT model, named after three eminent economists, Baumol, Allais, and Tobin, is the foundation for almost all cash management models in use today. The goal of the BAT model is to minimize the total costs involving the brokerage fees and the opportunity cost of interest lost on the cash held on hand. The brokerage fees are incurred in connection with the transactions for liquidating securities and converting them into cash. The opportunity cost of lost interest represents the income the firm could have earned by investing the cash in an interest-bearing asset instead of holding it on hand. In Chapter 1, a proof of the equivalency of the three seemingly different models of Baumol, Allais and Tobin is provided. The BAT model yields a square-root-formula that helps us determine the optimal level of cash to carry on hand.

In practice the square-root-formula of the BAT model often leads to fractional number of transactions involving the liquidation of securities and also fractional number of time periods (days or weeks) in the cycle-time between two consecutive transactions. Therefore, the results are not useful from a managerial or implementation point of view. Mathematical methods for obtaining integer solutions both for the number of transactions and the number of time periods between two consecutive transactions under different scenarios are described in Chapters 2 and 3.

In the basic version of the BAT model there is no provision for the use of short-term credit. However, in the case of individual persons as well as corporations, it is sometimes beneficial to borrow funds on a short-term basis and repay the loan as soon as the funds become available. An extended version of the BAT model that not only includes the flexibility of short-term borrowing as described in the Sastry-Ogden-Sundaram (SOS) model, but also incorporates the requirement for the firm to buy insurance on the maximum amount borrowed during any time interval is discussed in Chapter 4. Further, a generalized version of the BAT and SOS models with insurance requirement is presented in Chapter 5. These cash management models are often considered as derivatives of some of the optimization models well-known in the field of Inventory Control and Production Management. The similarities and differences between the two types of models are also highlighted in this Chapter.

A single-period stochastic-demand cash management model is discussed in Chapter 6. In this model, the demand for cash is random and cannot be predicted in advance, but some past data is available. A formula is developed for the optimal amount of cash to be kept on hand at the beginning of the period with the goal of minimizing the total expected cost, given the interest rate at the beginning of the period and the interest rate that may be charged by the bank when the funds are borrowed on an emergency basis, should such a need arise.

The BAT model is static in the sense that the parameter values remain constant from one period to the next. In contrast, in a multi-period dynamic (MPD) cash management model the transaction costs, interest rates and proportional charge rates vary from one period to the next. Mixed linear-integer programming techniques for solving the multi-period dynamic (MPD) cash management model are described in Chapter 7. Conclusions and suggestions for future research are presented in Chapter 8.

#### DOI

10.25777/d2w4-4y45

9798762199155

COinS