The Annals of Applied Probability

A Duality Method for Optimal Consumption and Investment Under Short-Selling Prohibition. II. Constant Market Coefficients

Gan-Lin Xu and Steven E. Shreve

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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.

Article information

Source
Ann. Appl. Probab., Volume 2, Number 2 (1992), 314-328.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005706

Digital Object Identifier
doi:10.1214/aoap/1177005706

Mathematical Reviews number (MathSciNet)
MR1161057

Zentralblatt MATH identifier
0773.90017

JSTOR
links.jstor.org

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 60G44: Martingales with continuous parameter 90A16 49B60

Keywords
Portfolio and consumption processes utility functions stochastic control martingale representation theorems duality

Citation

Xu, Gan-Lin; Shreve, Steven E. A Duality Method for Optimal Consumption and Investment Under Short-Selling Prohibition. II. Constant Market Coefficients. Ann. Appl. Probab. 2 (1992), no. 2, 314--328. doi:10.1214/aoap/1177005706. https://projecteuclid.org/euclid.aoap/1177005706


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See also

  • Part I: Gan-Lin Xu, Steven E. Shreve. A Duality Method for Optimal Consumption and Investment Under Short- Selling Prohibition. I. General Market Coefficients. Ann. Appl. Probab., Volume 2, Number 1 (1992), 87--112.