Consumption-portfolio optimization with recursive utility in incomplete markets
AbstractIn 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, Econometrica 60, 393–394, 1992 ) are not applicable. We provide new explicit solutions to the Bellman equation with Epstein–Zin preferences in an incomplete market for non-unit elasticity of intertemporal substitution (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. Copyright Springer-Verlag 2013
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Bibliographic InfoArticle provided by Springer in its journal Finance and Stochastics.
Volume (Year): 17 (2013)
Issue (Month): 1 (January)
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Web page: http://www.springerlink.com/content/101164/
Find related papers by JEL classification:
- 93E - - - - - -
- 91G - - - - - -
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- D91 - Microeconomics - - Intertemporal Choice - - - Intertemporal Household Choice; Life Cycle Models and Saving
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
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