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Knightian Uncertainty, k-Ignorance, and Optimal Timing

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  • Luis H. R. Alvarez

    () (Department of Economics, Turku School of Economics)

Abstract

We investigate within a continuous time setting how Knightian uncertainty characterized by k-ignorance affects the optimal timing policies of a risk-neutral and uncertainty averse investor in the case where the exercise payoff is monotonic. We prove that increased Knightian uncertainty unambiguously decreases the value of the optimal timing policy of an uncertainty averse investor. We also show that higher Knightian uncertainty accelerates timing by shrinking the continuation region whenever the termination payoff is independent of Knightian uncertainty. If this independence condition is not fulfilled, then our results indicate that higher Knightian uncertainty may decelerate optimal timing.

Suggested Citation

  • Luis H. R. Alvarez, 2007. "Knightian Uncertainty, k-Ignorance, and Optimal Timing," Discussion Papers 25, Aboa Centre for Economics.
  • Handle: RePEc:tkk:dpaper:dp25
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    File URL: http://www.ace-economics.fi/kuvat/dp025.pdf
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    References listed on IDEAS

    as
    1. Alvarez, Luis H. R., 1998. "Exit strategies and price uncertainty: a Greenian approach," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 43-56, January.
    2. Luis Alvarez & Rune Stenbacka, 2003. "Optimal risk adoption: a real options approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 123-147, December.
    3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    4. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2007. "Irreversible investment and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 136(1), pages 668-694, September.
    5. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    6. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    7. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 579-608.
    8. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Knightian uncertainty; k-ambiguity; optimal stopping; diffusions;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing

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