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August 2001 A dynamic maximum principle for the optimization of recursive utilities under constraints
N. El Karoui, S. Peng, M. C. Quenez
Ann. Appl. Probab. 11(3): 664-693 (August 2001). DOI: 10.1214/aoap/1015345345


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.


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N. El Karoui. S. Peng. M. C. Quenez. "A dynamic maximum principle for the optimization of recursive utilities under constraints." Ann. Appl. Probab. 11 (3) 664 - 693, August 2001.


Published: August 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1040.91038
MathSciNet: MR1865020
Digital Object Identifier: 10.1214/aoap/1015345345

Primary: 92E20
Secondary: 35B50 , 60J60

Keywords: Backward stochastic differential equations , forward-backward system , large investor , maximum principle , recursive utility , utility maximization

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.11 • No. 3 • August 2001
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