Optimal Lifetime Consumption-Portfolio Strategies Under Trading Constraints and Generalized Recursive Preferences

Stochastic Processes and their Applications, Vol. 108, pp. 155-202, December 2003

51 Pages Posted: 21 Nov 2002

Abstract

We consider the lifetime consumption-portfolio problem in a competitive securities market with essentially arbitrary continuous price dynamics, and convex trading constraints (e.g., incomplete markets and short-sale constraints). Abstract first-order conditions of optimality are derived, based on a preference-independent notion of constrained state pricing. For homothetic generalized recursive utility, we derive closed-form solutions for the optimal consumption and trading strategy in terms of the solution to a single constrained BSDE. Incomplete market solutions are related to complete markets solutions with modified risk aversion towards non-marketed risk. Methodologically, we develop the utility gradient approach, but for the homothetic case we also verify the solution using the dynamic programming approach, without having to assume a Markovian structure. Finally, we present a class of parametric examples in which the BSDE characterizing the solution reduces to a system of Riccati equations.

Keywords: Portfolio Choice, Recursive Utility, Optimal Consumption, Incomplete Markets, Short Sale Constraints

JEL Classification: D91, G11, G12, D11, D52, D81

Suggested Citation

Schroder, Mark D. and Skiadas, Costis, Optimal Lifetime Consumption-Portfolio Strategies Under Trading Constraints and Generalized Recursive Preferences. Stochastic Processes and their Applications, Vol. 108, pp. 155-202, December 2003. Available at SSRN: https://ssrn.com/abstract=346420 or http://dx.doi.org/10.2139/ssrn.346420

Mark D. Schroder

Michigan State University - The Eli Broad Graduate School of Management ( email )

323 Eppley Center
East Lansing, MI 48824-1121
United States
517-432-0622 (Phone)
517-432-1080 (Fax)

Costis Skiadas (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States
847-467-2328 (Phone)
847-491-5719 (Fax)

HOME PAGE: http://www.kellogg.northwestern.edu/faculty/skiadas/research/research.htm

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