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Optimal Multiperiod Investment-Consumption Policies

Robert A. Abrams
Uday S. Karmarkar

Abstract

We investigate the structure of optimal policies in general multiperiod multiasset consumption-investment problems in the presence of transfer costs. A number of objectives such as utility of a consumption stream, utility of terminal wealth, and multi-attribute utility are encompassed by the formulation. The general problem is first formulated as a stochastic dynamic program. The one-period subproblems are then analyzed using convex duality theory. The principal result is the characterization of a not necessarily convex "region of no transactions" for each period. If in any period the entering asset position is in this set, no transactions are made. Each point of the set side is the vertex of a cone such that if the entering asset position is outside the set, the optimal policy is to move to the vertex of the cone in which the entering asset position lies. It is shown that the region of no transactions is a connected set and that it is a cone when the utility function is assumed to be positively homogeneous. In the latter case, the optimal decision policy and induced utility functions are also positively homogeneous.