Consumption-Portfolio Optimization with Recursive Utility in Incomplete Markets
Goethe University Frankfurt
Frank Thomas Seifried
University of Kaiserslautern
University of Copenhagen
June 26, 2011
In an incomplete market we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein-Zin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton-Jacobi-Bellman equation and provide a suitable verification theorem. The proof of this verification theorem is complicated by the fact that the Epstein-Zin aggregator is non-Lipschitz, so standard verification results (e.g., in Duffie and Epstein (1992)) are not applicable. We provide new explicit solutions to the Bellman equation with Epstein-Zin preferences in an incomplete market for non-unit EIS and apply our verification result to prove that they solve the consumption-investment problem. We also compare our exact solutions to the Campbell-Shiller approximation and assess its accuracy.
Number of Pages in PDF File: 32
Keywords: consumption-portfolio optimization, recursive utility, stochastic control approach, stochastic volatility, unspanned state process, Campbell-Shiller approximation
JEL Classification: G11, D91, C61working papers series
Date posted: June 3, 2010 ; Last revised: June 28, 2011
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