A Two Asset Deterministic Cash Balance Problem

This paper considers a two-asset cash management problem in which transfers between the cash account and a portfolio of earning assets are used to control a cash account subject to a sequence of deterministic inflows and outflows. Transaction, holding and penalty costs are assumed to be concave and nondecreasing. A network approach is used to derive qualitative results which reduce the calculations required to find an optimal solution. For the special case of no backlogging, proportional holdings cost and transactions cost with a “lumpy” and proportional component, additional results including a planning horizon theorem are established. A numerical example is solved.