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Consumption-portfolio optimization with recursive utility in incomplete markets

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  • Holger Kraft

    ()

  • Frank Seifried

    ()

  • Mogens Steffensen

    ()

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    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

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 17 (2013)
    Issue (Month): 1 (January)
    Pages: 161-196

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    Handle: RePEc:spr:finsto:v:17:y:2013:i:1:p:161-196

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    Related research

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

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    References

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    1. Mark Schroder & Costis Skiadas, 2008. "Optimality And State Pricing In Constrained Financial Markets With Recursive Utility Under Continuous And Discontinuous Information," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 199-238.
    2. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
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    13. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, 08.
    14. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
    15. Harjoat S. Bhamra & Lars-Alexander Kuehn & Ilya A. Strebulaev, 2010. "The Levered Equity Risk Premium and Credit Spreads: A Unified Framework," Review of Financial Studies, Society for Financial Studies, vol. 23(2), pages 645-703, February.
    16. Ma, Chenghu, 2000. "An existence theorem of intertemporal recursive utility in the presence of Levy jumps," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 509-526, December.
    17. Schroder, Mark & Skiadas, Costis, 2003. "Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 155-202, December.
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