Optimal Multiperiod Investment-Consumption Policies
研究存在交易成本的多期多资产消费投资问题，利用凸对偶理论刻画最优策略，特别是每期不进行交易的资产持有区域，并证明该区域是连通的，在效用函数齐次时呈锥形。
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 multiattribute 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 of no for each period. If in any period the entering asset position is in this set, no transactions are made. Each point of the set 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 IN THIS PAPER we study a general class of multiperiod, multiasset investmentconsumption problems. Our purpose is to characterize the structure of optimal policies in the presence of transaction costs. Related problems have been studied by several authors, e.g., Constantinides [2, 3], Fama [5], Eppen and Fama [4], Kamin [7], Magill and Constantinides [10], Zabel [17], Hakansson [6], Merton [11], Samuelson [14], and Mukherjee and Zabel [12], and in these papers optimal policies have been characterized for a number of special cases. Our methodology significantly generalizes and sharpens many of the above results. For example, much of the previous work has been limited to the two-asset case or to particular utility functions, whereas our formulation allows any number of assets and general concave utility functions. The principal result of this paper, in the case of proportional transaction costs and concave utility functions, is the characterization of the optimal policy in each period and the set of entering asset positions from which no transactions should be made. This set or of no (RNT) can take on many forms ranging from a simple halfline to a nonconvex set. (See examples in Section 3.)