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Consumption-portfolio optimization with recursive utility in incomplete markets

  • Holger Kraft


  • Frank Seifried


  • Mogens Steffensen


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    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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    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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    1. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    2. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    3. 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.
    4. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    6. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
    7. 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.
    8. 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.
    9. Hall, Robert E, 1988. "Intertemporal Substitution in Consumption," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 339-57, April.
    10. Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
    11. 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.
    12. Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein, 2005. "Can Standard Preferences Explain the Prices of out of the Money S&P 500 Put Options," NBER Working Papers 11861, National Bureau of Economic Research, Inc.
    13. Costis Skiadas, 1998. "Recursive utility and preferences for information," Economic Theory, Springer, vol. 12(2), pages 293-312.
    14. 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.
    15. Schroder, Mark & Skiadas, Costis, 2005. "Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 1-30, January.
    16. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, 02.
    17. Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(01), pages 63-91, March.
    18. 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.
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