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Optimal Investment With Undiversifiable Income Risk

Author

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  • Darrell Duffie
  • Thaleia Zariphopoulou

Abstract

This paper treats the problem of consumption and portfolio choice in continuous time, with stochastic income that cannot be replicated by trading the available securities. the optimal controls and value functions are characterized in terms of the viscosity solution of the associated Hamilton-Jacobi-Bellman equation, which is shown to exist and is characterized. the optimal policy is then given from the first-order conditions of the Hamilton-Jacobi-Bellman equation. Copyright 1993 Blackwell Publishers.

Suggested Citation

  • Darrell Duffie & Thaleia Zariphopoulou, 1993. "Optimal Investment With Undiversifiable Income Risk," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 135-148.
  • Handle: RePEc:bla:mathfi:v:3:y:1993:i:2:p:135-148
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9965.1993.tb00083.x
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    Citations

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    Cited by:

    1. Vila, Jean-Luc & Zariphopoulou, Thaleia, 1997. "Optimal Consumption and Portfolio Choice with Borrowing Constraints," Journal of Economic Theory, Elsevier, vol. 77(2), pages 402-431, December.
    2. L. A. Bordag & I. P. Yamshchikov & D. Zhelezov, 2015. "Portfolio optimization in the case of an asset with a given liquidation time distribution," Post-Print hal-01186961, HAL.
    3. Suresh M. Sundaresan, 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    4. Bayraktar, Erhan & Young, Virginia R., 2007. "Minimizing the probability of lifetime ruin under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 196-221, July.
    5. Luigi Guiso & Tullio Jappelli, 1998. "Background Uncertainty and the Demand for Insurance Against Insurable Risks," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 23(1), pages 7-27, June.
    6. Moshe A. Milevsky & Virginia R. Young, 2015. "Annuitization and asset allocation," Papers 1506.05990, arXiv.org.
    7. Farhi, Emmanuel & Panageas, Stavros, 2007. "Saving and investing for early retirement: A theoretical analysis," Journal of Financial Economics, Elsevier, vol. 83(1), pages 87-121, January.
    8. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
    9. Erhan Bayraktar & Virginia Young, 2011. "Proving regularity of the minimal probability of ruin via a game of stopping and control," Finance and Stochastics, Springer, vol. 15(4), pages 785-818, December.
    10. Munk, Claus, 2000. "Optimal consumption/investment policies with undiversifiable income risk and liquidity constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(9), pages 1315-1343, August.
    11. Fehle, Frank, 2004. "A note on transaction costs and the existence of derivatives markets," Journal of Economics and Business, Elsevier, vol. 56(1), pages 63-70.
    12. Morten Tolver Kronborg, 2014. "Optimal Consumption and Investment with Labor Income and European/American Capital Guarantee," Risks, MDPI, Open Access Journal, vol. 2(2), pages 1-24, May.
    13. Moawia, Alghalith, 2010. "Forward dynamic utilities: a new model and new results," MPRA Paper 21074, University Library of Munich, Germany.
    14. repec:gam:jsusta:v:10:y:2018:i:4:p:1027-:d:138895 is not listed on IDEAS
    15. Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
    16. Ljudmila A. Bordag & Ivan P. Yamshchikov & Dmitry Zhelezov, 2014. "Portfolio optimization in the case of an asset with a given liquidation time distribution," Papers 1407.3154, arXiv.org.
    17. Ljudmila A. Bordag & Ivan P. Yamshchikov, 2015. "Optimization problem for a portfolio with an illiquid asset: Lie group analysis," Papers 1512.06295, arXiv.org.
    18. Regis Houssou & Olivier Besson, 2010. "Indifference of Defaultable Bonds with Stochastic Intensity models," Papers 1003.4118, arXiv.org.
    19. Henderson, Vicky, 2005. "Explicit solutions to an optimal portfolio choice problem with stochastic income," Journal of Economic Dynamics and Control, Elsevier, vol. 29(7), pages 1237-1266, July.
    20. Adriana Ocejo, 2018. "Explicit solutions to utility maximization problems in a regime-switching market model via Laplace transforms," Papers 1804.08442, arXiv.org.
    21. Claus Munk, 1997. "Optimal Consumption/Investment Policies with Undiversifiable Income Risk and Borrowing Constraints," Finance 9712003, EconWPA.
    22. Bacinello, Anna Rita, 2000. "Valuation of contingent-claims characterising particular pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 177-188, October.
    23. Wiebke Wittmüß, 2006. "Robust Optimization of Consumption with Random Endowment," SFB 649 Discussion Papers SFB649DP2006-063, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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