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Investment under ambiguity with the best and worst in mind

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Abstract

Recent literature on optimal investment has stressed the difference between the impact of risk and the impact of ambiguity—also called Knightian uncertainty—on investors’ decisions. In this paper, we show that a decision maker’s attitude towards ambiguity is similarly crucial for investment decisions. We capture the investor’s individual ambiguity attitude by applying α-MEU preferences to a standard investment problem. We show that the presence of ambiguity often leads to an increase in the subjective project value, and entrepreneurs are more eager to invest. Thereby, our investment model helps to explain differences in investment behavior in situations which are objectively identical.

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References

  1. Ahn, D., Choi, S., Gale, D., Kariv, S.: Estimating ambiguity aversion in a portfolio choice experiment. UC Berkeley Working Paper (2007)

  2. Al-Najjar N.I., Weinstein J.: The ambiguity aversion literature: a critical assessment. Econ. Philos. 25, 249–284 (2009)

    Article  Google Scholar 

  3. Asano, T.: Irreversibilities and the optimal timing of environmental policy under knightian uncertainty. Discussion paper No. 643, Institute of Social and Economic Research at Osaka University (2005)

  4. Bhidé A.V.: The Origin and Evolution of New Business. Oxford University Press, Oxford (2000)

    Google Scholar 

  5. Chateauneuf A., Eichberger J., Grant S.: Choice under uncertainty with the best and worst in mind: neo-additive capacities. J. Econ. Theory 137, 538–567 (2007)

    Article  MATH  Google Scholar 

  6. Chen Z., Epstein L.: Ambiguity, risk, and asset returns in continuous time. Econometrica 70(4), 1403–1443 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Choi, U.J., Kim, K., Kwak, M.: Investment under ambiguity and regime-switching environment. Working paper, Korea Advanced Institute of Science and Technology (KAIST) (2009)

  8. DeBondt, W.F., Thaler, R.H.: Financial decision-making in markets and firms: a behavioral perspective. In: Handbook in Operations Research and Management Science: Finance, pp. 385–410. Elsevier, Amsterdam (1995)

  9. Dixit A.K., Pindyck R.S.: Investment Under Uncertainty. Princeton University Press, Princeton (1994)

    Google Scholar 

  10. Duffie D.: Dynamic Asset Pricing Theory, 3rd edn. Princeton University Press, Princeton (2001)

    MATH  Google Scholar 

  11. Economist: The R-Word. The Econ. 359(8216), 106 (2001)

  12. Ellsberg D.: Risk, ambiguity and the savage axioms. Quart. J. Econ. 75(4), 643–669 (1961)

    Article  Google Scholar 

  13. Epstein L.G., Schneider M.: IID: independently and indistinguishable distributed. J. Econ. Theory 113(1), 32–50 (2003a)

    Article  MathSciNet  MATH  Google Scholar 

  14. Epstein L.G., Schneider M.: Recursive multiple-priors. J. Econ. Theory 113(1), 1–31 (2003b)

    Article  MathSciNet  MATH  Google Scholar 

  15. Epstein L.G., Schneider M.: Ambiguity, information quality and asset pricing. J. Finance 63(1), 197–228 (2008)

    Article  Google Scholar 

  16. Epstein L.G., Wang T.: Intertemporal asset pricing under knightian uncertainty. Econometrica 62(3), 283–322 (1994)

    Article  MATH  Google Scholar 

  17. Ghiradato P., Maccheroni F., Marinacci M.: Differentiating ambiguity and ambiguity attitude. J. Econ. Theory 118, 133–173 (2004)

    Article  Google Scholar 

  18. Gilboa I., Schmeidler D.: Maxmin expected utility with non-unique prior. J. Math. Econ. 18, 141–153 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gysler, M., Kruse, J.B., Schubert, R.: Ambiguity and gender differences in financial decision making: an experimental examination of competence and confidence effects. Center for Economic Research, Swiss Federal Insitute of Technology, working paper (2002)

  20. Hannay E., Klibanoff P.: Updating preferences with multiple priors. Theor. Econ. 2, 261–298 (2006)

    Google Scholar 

  21. Heath C., Tversky A.: Preference and belief: ambiguity and competence in choice under uncertainty. J. Risk Uncertain. 4(1), 5–28 (1991)

    Article  MATH  Google Scholar 

  22. Hurwicz, L.: Optimality criteria for decision making under ignorance. Cowles Communication Discussion Paper, Statistics No. 370 (1951)

  23. Karatzas I., Kou S.G.: Hedging american contigent claims with constraint portfolios. Finance Stoch. 2, 215–258 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kilka M., Weber M.: What determines the shape of the probability weighting function under uncertainty?. Manage. Sci. 47, 1712–1726 (1998)

    Article  Google Scholar 

  25. Klibanoff P., Marinacci M., Mukerji S.: A smooth model of decision making under ambiguity. Econometrica 73(6), 1849–1892 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  26. Klibanoff P., Marinacci M., Mukerji S.: Recursive smooth ambiguity preferences. J. Econ. Theory 144(3), 930–976 (2009)

    Article  MATH  Google Scholar 

  27. Knight F.H.: Risk, Uncertainty, and Profit. Houghton Mifflin Company, Boston, MA (1921)

    Google Scholar 

  28. Kopylov, I.: Subjective probability and confidence. Working paper University of California, Irvine, (2008)

  29. Marinacci M.: Probabilistic sophistication and multiple priors. Econometrica 70(2), 755–764 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  30. McDonald R., Siegel D.: The value of waiting to invest. Quart. J. Econ. 101(4), 707–728 (1986)

    Article  Google Scholar 

  31. Miao, J., Wang, N.: Risk, uncertainty, and option exercise. Working paper Boston University and Columbia Business School (2007)

  32. Nishimura K.G., Ozaki H.: An axiomatic approach to \({\epsilon}\)-contamination. Econ. Theory 27, 333–340 (2004a)

    Article  MathSciNet  Google Scholar 

  33. Nishimura K.G., Ozaki H.: Search and knightian uncertainty. J. Econ. Theory 119(2), 299–333 (2004b)

    Article  MathSciNet  MATH  Google Scholar 

  34. Nishimura K.G., Ozaki H.: Irreversible investment and knightian uncertainty. J. Econ. Theory 136(1), 668–694 (2007)

    Article  MATH  Google Scholar 

  35. Olszewski W.: Preferences over sets of lotteries. Rev. Econ. Stud. 74, 567–595 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  36. Riedel F.: Optimal stopping with multiple priors. Econometrica 77(3), 857–908 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  37. Roubaud, D., Lapied, A., Kast, R.: Real options under ambiguity. working paper (2010)

  38. Sarin R., Wakker P.: Dynamic choice and non expected utility. J. Risk Uncertain. 17, 87–119 (1998)

    Article  MATH  Google Scholar 

  39. Savage L.J.: The Foundations of Statistics. Wiley, New York (1954)

    MATH  Google Scholar 

  40. Schmeidler D.: Subjective probability and expected utility without additivity. Econometrica 57(3), 571–587 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  41. Skiadas, C.: Smooth ambiguity aversion towards small risks and continuous-time recursive utility. Working paper (2008)

  42. Trojanowska M., Kort P.M.: The worst case for real options. J. Optim. Theory Appl. 146(3), 709–734 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Birkbeck College, University of London, Malet Street, Bloomsbury, London, WC1E 7HX, UK

    David Schröder

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  1. David Schröder
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Correspondence to David Schröder.

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Schröder, D. Investment under ambiguity with the best and worst in mind. Math Finan Econ 4, 107–133 (2011). https://doi.org/10.1007/s11579-011-0036-3

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  • DOI: https://doi.org/10.1007/s11579-011-0036-3

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