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A duality method for optimal consumption and investment under short- selling prohibition. II: Constant market coefficients. (English) Zbl 0773.90017

Summary: [For part I see the authors, Ann. Appl. Probab. 2, No. 1, 87-112 (1992; Zbl 0745.93083).]

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 I. 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.

MSC:
91B42Consumer behavior, demand theory
93E20Optimal stochastic control (systems)