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Optimal consumption and investment with Epstein–Zin recursive utility

Author

Listed:
  • Holger Kraft

    (Goethe University)

  • Thomas Seiferling

    (University of Kaiserslautern)

  • Frank Thomas Seifried

    (University of Trier)

Abstract

We study continuous-time optimal consumption and investment with Epstein–Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton–Jacobi–Bellman equation by a fixed point argument and makes it possible to compute both the indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.

Suggested Citation

  • Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:1:d:10.1007_s00780-016-0316-0
    DOI: 10.1007/s00780-016-0316-0
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    References listed on IDEAS

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    More about this item

    Keywords

    Consumption-portfolio choice; Asset pricing; Stochastic differential utility; Incomplete markets; Fixed point approach; FBSDE;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • 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
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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