Three Asset Cash Balance and Dynamic Portfolio Problems

This paper describes the form of the optimal operating policy for a three asset cash balance problem in which (1) holding and penalty costs are proportional to the level of the cash balance, (2) the costs incurred in transferring funds between cash and earning assets are proportional to the amount of funds transferred, and (3) inflows and outflows of cash are to some extent random. There are assumed to be two earning assets, called “bonds” and “stock,” that can be used to change the level of cash. “Stock” assets are the major source of the firm's earnings, and they are assumed to have higher expected returns per period than bonds but also to have higher transactions costs. The major concern, then, is with how “bonds” should be used as a buffer against random fluctuations in the cash account.