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Ambiguity, Risk and Portfolio Choice under Incomplete Information

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  • Jianjun Miao

    (Department of Economics, Boston University)

Abstract

This paper studies optimal consumption and portfolio choice in a Mertonstyle model with incomplete information when there is a distinction between ambiguity and risk. The latter distinction is afforded by adoption of recursive multiple-priors utility. The fundamental issues are: (i) How does the agent optimally estimate the unobservable processes as new information arrives over time? (ii) What are the effects of ambiguity and incomplete information on behavior? This paper shows that it is optimal to first use any prior to perform Bayesian estimation and then to maximize expected utility with that prior based on the resulting estimates. Finally, the paper shows that a hedging demand arises that is affected by both ambiguity and estimation risk.

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Bibliographic Info

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

Volume (Year): 10 (2009)
Issue (Month): 2 (November)
Pages: 257-279

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Handle: RePEc:cuf:journl:y:2009:v:10:i:2:p:257-279

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Related research

Keywords: Ambiguity; Recursive multiple-priors utility; Incomplete information; Portfolio choice; Hedging; Estimation risk;

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References

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  1. 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.
  2. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
  3. Larry G. Epstein & JianJun Miao, 2001. "A Two-Person Dynamic Equilibrium under Ambiguity," RCER Working Papers 478, University of Rochester - Center for Economic Research (RCER).
  4. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
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  6. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
  7. Feldman, David, 1992. "Logarithmic Preferences, Myopic Decisions, and Incomplete Information," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(04), pages 619-629, December.
  8. Xia, Yihong, 2000. "Learning About Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation," University of California at Los Angeles, Anderson Graduate School of Management qt3167f8mz, Anderson Graduate School of Management, UCLA.
  9. Zengjing Chen & Larry G. Epstein, 2000. "Ambiguity, risk and asset returns in continuous time," RCER Working Papers 474, University of Rochester - Center for Economic Research (RCER).
  10. Feldman, David, 1986. " Optimal Portfolio Choice under Incomplete Information: Discussion," Journal of Finance, American Finance Association, vol. 41(3), pages 747-49, July.
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  12. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 77-97, August.
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  16. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
  17. Gennotte, Gerard, 1986. " Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-46, July.
  18. Hansen, Lars Peter & Sargent, Thomas J. & Turmuhambetova, Gauhar & Williams, Noah, 2006. "Robust control and model misspecification," Journal of Economic Theory, Elsevier, vol. 128(1), pages 45-90, May.
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Citations

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Cited by:
  1. Nengjiu Ju & Jianjun Miao, . "Ambiguity, Learning, and Asset Returns," Boston University - Department of Economics - Working Papers Series wp2009-014, Boston University - Department of Economics.
  2. Miao, Jianjun & Wang, Neng, 2011. "Risk, uncertainty, and option exercise," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 442-461, April.
  3. Dai, Darong, 2011. "Modeling the minimum time needed to economic maturity," MPRA Paper 40583, University Library of Munich, Germany, revised 08 Aug 2012.
  4. Massimo Guidolin & Francesca Rinaldi, 2011. "Ambiguity in Asset Pricing and Portfolio Choice: A Review of the Literature," Working Papers 417, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  5. Weidong Xu & Hongyi Li & Chongfeng Wu, 2011. "A Robust General Equilibrium Stochastic Volatility Model with Recursive Preference Investors," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 217-231, November.
  6. Hui Chen & Nengjiu Ju & Jianjun Miao, . "Dynamic Asset Allocation with Ambiguous Return Predictability," Boston University - Department of Economics - Working Papers Series wp2009-015, Boston University - Department of Economics.
  7. Martin Schneider, 2010. "The Research Agenda: Martin Schneider on Multiple Priors Preferences and Financial Markets," EconomicDynamics Newsletter, Review of Economic Dynamics, vol. 11(2), April.
  8. Junfeng Qiu, 2011. "Bank money, aggregate liquidity, and asset prices," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 295-346, November.
  9. Hui Huang & Shunming Zhang, 2011. "The Distorted Theory of Rank-Dependent Expected Utility," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 233-263, November.
  10. Liu, Hening, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 623-640, April.

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