This paper examines the continuous-time portfolio-consumption
problem of an agent with a recursive utility in the presence of nonlinear
constraints on the wealth.Using backward stochastic differential equations, we
state a dynamic maximum principle which generalizes the characterization of
optimal policies obtained by Duffie and Skiadas [J.Math Econ. 23,
107 –131 (1994)] in the case of a linear wealth. From this property, we
derive a characterization of optimal wealth and utility processes as the unique
solution of a forward-backward system. Existence of an optimal policy is also
established via a penalization method.
Publié le : 2001-08-14
Classification:
Utility maximization,
recursive utility,
large investor,
backward stochastic differential equations,
maximum principle,
forward-backward system,
92E20,
60J60,
35B50
@article{1015345345,
author = {El Karoui, N. and Peng, S. and Quenez, M. C.},
title = {A dynamic maximum principle for the optimization of recursive
utilities under constraints},
journal = {Ann. Appl. Probab.},
volume = {11},
number = {2},
year = {2001},
pages = { 664-693},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345345}
}
El Karoui, N.; Peng, S.; Quenez, M. C. A dynamic maximum principle for the optimization of recursive
utilities under constraints. Ann. Appl. Probab., Tome 11 (2001) no. 2, pp. 664-693. http://gdmltest.u-ga.fr/item/1015345345/