Authors
Gan-Lin Xu, Steven E Shreve
Publication date
1992/5/1
Journal
The Annals of Applied Probability
Pages
314-328
Publisher
Institute of Mathematical Statistics
Description
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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Scholar articles
GL Xu, SE Shreve - The Annals of Applied Probability, 1992