This paper extends He and Pearson's (1991) martingale approach to the study of optimal intertemporal consumption and portfolio policies with incomplete markets and short‐sale constraints to a framework in which no assumptions are made on the price process for the securities. We show how both their characterization of the budget‐feasible set and duality result can be extended to account for an unbounded set II of Arrow‐Debreu state prices compatible with the arbitrage‐free assumption. We also supply a (fairly general) sufficient condition for II to be bounded, as required in their setting.
Consumption and Portfolio Policies with Incomplete Markets and Short-Sales Constraints in the Finite Dimensional Case: Some Remarks
ORTU, FULVIO
1994
Abstract
This paper extends He and Pearson's (1991) martingale approach to the study of optimal intertemporal consumption and portfolio policies with incomplete markets and short‐sale constraints to a framework in which no assumptions are made on the price process for the securities. We show how both their characterization of the budget‐feasible set and duality result can be extended to account for an unbounded set II of Arrow‐Debreu state prices compatible with the arbitrage‐free assumption. We also supply a (fairly general) sufficient condition for II to be bounded, as required in their setting.
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