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Optimal Investment With Undiversifiable Income Risk

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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.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 3 (1993)
Issue (Month): 2 ()
Pages: 135-148

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Handle: RePEc:bla:mathfi:v:3:y:1993:i:2:p:135-148

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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Erhan Bayraktar & Virginia R. Young, 2007. "Minimizing the Probability of Lifetime Ruin under Borrowing Constraints," Papers math/0703850, arXiv.org.
  5. Luigi Guiso & Tullio Jappelli, 1998. "Background Uuncertainty and the Demand for Insurance against Insurable Risks," CSEF Working Papers 02, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  6. Moawia, Alghalith, 2010. "Forward dynamic utilities: a new model and new results," MPRA Paper 21074, University Library of Munich, Germany.
  7. Regis Houssou & Olivier Besson, 2010. "Indifference of Defaultable Bonds with Stochastic Intensity models," Papers 1003.4118, arXiv.org.
  8. 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.
  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. Claus Munk, 1997. "Optimal Consumption/Investment Policies with Undiversifiable Income Risk and Borrowing Constraints," Finance 9712003, EconWPA.
  11. 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.
  12. 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.
  13. 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.
  14. Bacinello, Anna Rita, 2000. "Valuation of contingent-claims characterising particular pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 177-188, October.
  15. 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.
  16. Wiebke Wittmüß, 2006. "Robust Optimization of Consumption with Random Endowment," SFB 649 Discussion Papers SFB649DP2006-063, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  17. 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 171-194, May.

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