Xu, Gan-Lin; Shreve, Steven E. A duality method for optimal consumption and investment under short- selling prohibition. II: Constant market coefficients. (English) Zbl 0773.90017 Ann. Appl. Probab. 2, No. 2, 314-328 (1992). 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. Cited in 33 Documents MSC: 91B42 Consumer behavior, demand theory 93E20 Optimal stochastic control Keywords:continuous-time, consumption/investment problem Citations:Zbl 0745.93083 PDFBibTeX XMLCite \textit{G.-L. Xu} and \textit{S. E. Shreve}, Ann. Appl. Probab. 2, No. 2, 314--328 (1992; Zbl 0773.90017) Full Text: DOI