Abstract: Characterizations of Exchange Convertibility Schemes: A Structure for Analysis

This paper extends the results of previous work by the author in the development of a structure for analysis of rather general two-currency decision problems using an nstage dynamic programming model. After a brief review of the model, the paper provides a characterization of a convertibility scheme as a set function which assigns to each currency portfolio a set of currency portfolios which can be attained from the original portfolio, operating through the convertibility scheme. The concept of a substitutable convertibility scheme is developed; the substitutability property allows the decision maker to substitute a functionally determined single currecy payoff for a given twocurrency payoff. Two tests to determine substitutability in general, and for a particular return function, are developed. The modest reduction in dimensionality of the dynamic programming problem arising from this property is explained. Some specific convertibility schemes are then characterized, including free convertibility, inconvertibility, retention quotas, maximum balance, maximum acquisition, and multiple rate schemes. The substitutability of free convertibility is demonstrated. A retention quota scheme which allows free sale and purchase of retained funds in a parallel market is shown to be equivalent to a free convertibility scheme, and therefore substitutable.