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May, 1992 A Duality Method for Optimal Consumption and Investment Under Short-Selling Prohibition. II. Constant Market Coefficients
Gan-Lin Xu, Steven E. Shreve
Ann. Appl. Probab. 2(2): 314-328 (May, 1992). DOI: 10.1214/aoap/1177005706

Abstract

A continuous-time, consumption/investment problem with constant market coefficients is considered on a finite horizon. A dual problem is defined along the lines of Part 1. The value functions for both problems are proved to be solutions to the corresponding Hamilton-Jacobi-Bellman equations and are provided in terms of solutions to linear, second-order, partial differential equations. As a consequence, a mutual fund theorem is obtained in this market, despite the prohibition of short-selling. If the utility functions are of power form, all these results take particularly simple forms.

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Gan-Lin Xu. Steven E. Shreve. "A Duality Method for Optimal Consumption and Investment Under Short-Selling Prohibition. II. Constant Market Coefficients." Ann. Appl. Probab. 2 (2) 314 - 328, May, 1992. https://doi.org/10.1214/aoap/1177005706

Information

Published: May, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0773.90017
MathSciNet: MR1161057
Digital Object Identifier: 10.1214/aoap/1177005706

Subjects:
Primary: 93E20
Secondary: 49B60 , 60G44 , 90A16

Keywords: Duality , martingale representation theorems , Portfolio and consumption processes , Stochastic control , utility functions

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.2 • No. 2 • May, 1992
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