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Fuzzy measures and asset prices: accounting for information ambiguity

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  • Umberto Cherubini

Abstract

A recent stream of literature has suggested that many market imperfections or 'puzzles' can be easily explained once information ambiguity, or knightian uncertainty is taken into account. Here we propose a parametric representation of this concept by means of a special class of fuzzy measures, known as gλ-measures. The parameter λ may be considered an indicator of uncertainty. Starting with a distribution, a value λ in (0, ∞) and a benchmark utility function we obtain a sub-additive expected utility, representing uncertainty aversion. A dual value λ* in (-1, 0) defining a super-additive expected utility is also recovered, while the benchmark expected utility is obtained for λ = λ* = 0. The two measures may be considered as lower and upper bounds of expected utility with respect to a set of probability measures, in the spirit of Gilboa-Schmeidler MMEU theory and of Dempster probability interval approach. The parametrization may be used to determine the effect of information ambiguity on asset prices in a very straightforward way. As examples, we determine the price of a corporate debt contract and a 'fuzzified' version of the Black and Scholes model.

Suggested Citation

  • Umberto Cherubini, 1997. "Fuzzy measures and asset prices: accounting for information ambiguity," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(3), pages 135-149.
    • Handle: RePEc:taf:apmtfi:v:4:y:1997:i:3:p:135-149
    DOI: 10.1080/135048697334773
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    1. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    2. Gilboa, Itzhak, 1985. "Duality in Non-Additive Expected Utility Theory," Foerder Institute for Economic Research Working Papers 275390, Tel-Aviv University > Foerder Institute for Economic Research.
    3. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    4. Dow, James & da Costa Werlang, Sergio Ribeiro, 1992. "Excess volatility of stock prices and Knightian uncertainty," European Economic Review, Elsevier, vol. 36(2-3), pages 631-638, April.
    5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    6. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-1272, November.
    7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    8. Karni, Edi & Schmeidler, David, 1990. "Utility Theory and Uncertainty," Foerder Institute for Economic Research Working Papers 275480, Tel-Aviv University > Foerder Institute for Economic Research.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    11. Camerer, Colin & Weber, Martin, 1992. "Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-370, October.
    12. Jie Hu, 1994. "Market breakdowns and price crashes explained by information ambiguity," FRB Atlanta Working Paper 94-13, Federal Reserve Bank of Atlanta.
    13. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    14. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    15. repec:dau:papers:123456789/5630 is not listed on IDEAS
    16. repec:crs:wpaper:9513 is not listed on IDEAS
    17. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    18. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    19. Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(1), pages 21-52.
    20. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
    21. Karni, Edi & Schmeidler, David, 1991. "Utility theory with uncertainty," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 33, pages 1763-1831, Elsevier.
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    4. Muzzioli, S. & Torricelli, C., 2005. "The pricing of options on an interval binomial tree. An application to the DAX-index option market," European Journal of Operational Research, Elsevier, vol. 163(1), pages 192-200, May.

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