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Consumption-portfolio optimization with recursive utility in incomplete markets

Author

Listed:
  • Holger Kraft
  • Frank Seifried
  • Mogens Steffensen

Abstract

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, 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

Suggested Citation

  • Holger Kraft & Frank Seifried & Mogens Steffensen, 2013. "Consumption-portfolio optimization with recursive utility in incomplete markets," Finance and Stochastics, Springer, vol. 17(1), pages 161-196, January.
    • Handle: RePEc:spr:finsto:v:17:y:2013:i:1:p:161-196
    DOI: 10.1007/s00780-012-0184-1
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    References listed on IDEAS

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    More about this item

    Keywords

    Consumption-portfolio optimization; Recursive utility; Stochastic control approach; Stochastic volatility; Unspanned state process; Campbell–Shiller approximation; 93E20; 91G10; G11; D91; C61;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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