A Duality Method for Optimal Consumption and Investment Under Short-Selling Prohibition. II. Constant Market Coefficients
Xu, Gan-Lin ; Shreve, Steven E.
Ann. Appl. Probab., Tome 2 (1992) no. 4, p. 314-328 / Harvested from Project Euclid
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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.
Publié le : 1992-05-14
Classification:  Portfolio and consumption processes,  utility functions,  stochastic control,  martingale representation theorems,  duality,  93E20,  60G44,  90A16,  49B60 
@article{1177005706,
     author = {Xu, Gan-Lin and Shreve, Steven E.},
     title = {A Duality Method for Optimal Consumption and Investment Under Short-Selling Prohibition. II. Constant Market Coefficients},
     journal = {Ann. Appl. Probab.},
     volume = {2},
     number = {4},
     year = {1992},
     pages = { 314-328},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177005706}
}

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., Tome 2 (1992) no. 4, pp.  314-328. http://gdmltest.u-ga.fr/item/1177005706/