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Optimal Stopping of Active Portfolio Management

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  • Kyoung Jin Choi

    ()
    (Department of Mathematics, KAIST, Korea Advanced Institute of Science and Technology)

  • Hyeng Keun Koo

    ()
    (School of Business Administration, Ajou University)

  • Do Young Kwak

    ()
    (Department of Mathematics, KAIST)

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    Abstract

    We study an investor¡¯s decision to switch from active portfolio management to passive management. This problem is mathematically modelled by a mixture of a consumption-portfolio selection problem and an optimal stopping problem. We assume that the investor has stochastic differential utility with ambiguity aversion and incurs utility loss from active portfolio management that can be avoided by switching to passive management, and show that she manages actively as long as her level of wealth is above a certain threshold. The threshold wealth level is shown to be an increasing function of both the coefficient of ambiguity aversion and the utility cost of active management.

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    Bibliographic Info

    Article provided by Society for AEF in its journal Annals of Economics and Finance.

    Volume (Year): 5 (2004)
    Issue (Month): 1 (May)
    Pages: 93-126

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    Handle: RePEc:cuf:journl:y:2004:v:5:i:1:p:93-126

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    Related research

    Keywords: Consumption-portfolio selection; Active management; Passive management; Discretionary stopping time; Recursive utility; Stochastic differential utility; Optimal switching; Ambiguity;

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    References

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    1. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-36.
    2. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 21(6), pages 577-606.
    3. Costis Skiadas, 1998. "Recursive utility and preferences for information," Economic Theory, Springer, Springer, vol. 12(2), pages 293-312.
    4. Haliassos, Michael & Bertaut, Carol C, 1995. "Why Do So Few Hold Stocks?," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 105(432), pages 1110-29, September.
    5. Domenico Cuoco & Jaksa Cvitanic, . "Optimal Consumption Choices for a "Large" Investor," Rodney L. White Center for Financial Research Working Papers, Wharton School Rodney L. White Center for Financial Research 04-96, Wharton School Rodney L. White Center for Financial Research.
    6. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, Elsevier, vol. 49(1), pages 33-83, October.
    7. Epstein Larry G. & Wang Tan, 1995. "Uncertainty, Risk-Neutral Measures and Security Price Booms and Crashes," Journal of Economic Theory, Elsevier, Elsevier, vol. 67(1), pages 40-82, October.
    8. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 353-94, March.
    9. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(1), pages 1-71.
    10. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    11. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, Econometric Society, vol. 70(4), pages 1403-1443, July.
    12. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, Econometric Society, vol. 41(5), pages 867-87, September.
    13. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, Elsevier, vol. 89(1), pages 68-126, November.
    14. 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, Econometric Society, vol. 57(4), pages 937-69, July.
    15. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, Econometric Society, vol. 62(2), pages 283-322, March.
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    Cited by:
    1. Xiongfei Jian & Xun Li & Fahuai Yi, 2014. "Optimal Investment with Stopping in Finite Horizon," Papers 1406.6940, arXiv.org.

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