The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 11, Number 3 (2001), 664-693.
A dynamic maximum principle for the optimization of recursive utilities under constraints
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.
Ann. Appl. Probab., Volume 11, Number 3 (2001), 664-693.
First available in Project Euclid: 5 March 2002
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El Karoui, N.; Peng, S.; Quenez, M. C. A dynamic maximum principle for the optimization of recursive utilities under constraints. Ann. Appl. Probab. 11 (2001), no. 3, 664--693. doi:10.1214/aoap/1015345345. https://projecteuclid.org/euclid.aoap/1015345345