Technical Note—An Unexpected Stochastic Dominance: Pareto Distributions, Dependence, and Diversification

Published Online:https://doi.org/10.1287/opre.2022.0505

References

  • Alam K, Saxena KML (1981) Positive dependence in multivariate distributions. Comm. Statist. Theory Methods 10(12):1183–1196.CrossrefGoogle Scholar
  • Albrecher H, Asmussen S, Kortschak D (2006) Tail asymptotics for the sum of two heavy-tailed dependent risks. Extremes 9(2):107–130.CrossrefGoogle Scholar
  • Andriani P, McKelvey B (2007) Beyond Gaussian averages: Redirecting international business and management research toward extreme events and power laws. J. Internat. Bus. Stud. 38(7):1212–1230.CrossrefGoogle Scholar
  • Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.CrossrefGoogle Scholar
  • Balkema A, de Haan L (1974) Residual life time at great age. Ann. Probability 2:792–804.CrossrefGoogle Scholar
  • Baucells M, Heukamp FH (2006) Stochastic dominance and cumulative prospect theory. Management Sci. 52(9):1409–1423.LinkGoogle Scholar
  • Bauer D, Zanjani G (2016) The marginal cost of risk, risk measures, and capital allocation. Management Sci. 62(5):1431–1457.LinkGoogle Scholar
  • Block HW, Savits TH, Shaked M (1982) Some concepts of negative dependence. Ann. Probability 10(3):765–772.CrossrefGoogle Scholar
  • Block HW, Savits TH, Shaked M (1985) A concept of negative dependence using stochastic ordering. Statist. Probability Lett. 3(2):81–86.CrossrefGoogle Scholar
  • Caballé J, Pomansky A (1996) Mixed risk aversion. J. Econom. Theory 71(2):485–513.CrossrefGoogle Scholar
  • Chew SH, Karni E, Safra Z (1987) Risk aversion in the theory of expected utility with rank dependent probabilities. J. Econom. Theory 42:370–381.CrossrefGoogle Scholar
  • Cheynel E, Cianciaruso D, Zhou F (2023) Fraud power laws. J. Accounting Res., ePub ahead of print September 30, https://doi.org/10.1111/1475-679X.12520.Google Scholar
  • de Haan L, Ferreira A (2006) Extreme Value Theory: An Introduction (Springer, Berlin).CrossrefGoogle Scholar
  • Embrechts P, Puccetti G (2010) Risk aggregation. Jaworski P, Durante F, Härdle W, Rychlik T, eds. Copula Theory and Its Applications (Springer, Berlin), 111–126.CrossrefGoogle Scholar
  • Embrechts P, Klüppelberg C, Mikosch T (1997) Modelling Extremal Events for Insurance and Finance (Springer, Heidelberg, Germany).CrossrefGoogle Scholar
  • Embrechts P, Lambrigger D, Wüthrich M (2009) Multivariate extremes and the aggregation of dependent risks: Examples and counter-examples. Extremes 12(2):107–127.CrossrefGoogle Scholar
  • Embrechts P, McNeil A, Straumann D (2002) Correlation and dependence in risk management: Properties and pitfalls. Dempster M, ed. Risk Management: Value at Risk and Beyond (Cambridge University Press, Cambridge, UK), 176–223.Google Scholar
  • Embrechts P, Resnick SI, Samorodnitsky G (1999) Extreme value theory as a risk management tool. North Amer. Actuarial J. 3(2):30–41.CrossrefGoogle Scholar
  • Fama EF, Miller MH (1972) The Theory of Finance (Dryden Press, Hinsdale).Google Scholar
  • Föllmer H, Schied A (2016) Stochastic Finance. An Introduction in Discrete Time, 4th ed. (Walter de Gruyter, Berlin).CrossrefGoogle Scholar
  • Gabaix X (2009) Power laws in economics and finance. Annu. Rev. Econom. 1(1):255–294.CrossrefGoogle Scholar
  • Hadar J, Russell WR (1969) Rules for ordering uncertain prospects. Amer. Econom. Rev. 59(1):25–34.Google Scholar
  • Hadar J, Russell WR (1971) Stochastic dominance and diversification. J. Econom. Theory 3(3):288–305.CrossrefGoogle Scholar
  • Hofert M, Wüthrich MV (2012) Statistical review of nuclear power accidents. Asia-Pacific J. Risk Insurance 7(1):1–20.Google Scholar
  • Huang RJ, Tzeng LY, Zhao L (2020) Fractional degree stochastic dominance. Management Sci. 66(10):4630–4647.LinkGoogle Scholar
  • Ibragimov R (2005) New majorization theory in economics and martingale convergence results in econometrics. PhD dissertation, Yale University, New Haven, CT.Google Scholar
  • Ibragimov R (2009) Portfolio diversification and value at risk under thick-tailedness. Quant. Finance 9(5):565–580.CrossrefGoogle Scholar
  • Ibragimov R, Prokhorov A (2017) Heavy Tails and Copulas: Topics in Dependence Modelling in Economics and Finance (World Scientific, Singapore).CrossrefGoogle Scholar
  • Ibragimov R, Walden J (2007) The limits of diversification when losses may be large. J. Bank. Finance 31(8):2551–2569.CrossrefGoogle Scholar
  • Ibragimov R, Walden J (2008) Portfolio diversification under local and moderate deviations from power laws. Insurance Math. Econom. 42(2):594–599.CrossrefGoogle Scholar
  • Ibragimov R, Walden J (2010) Optimal bundling strategies under heavy-tailed valuations. Management Sci. 56(11):1963–1976.LinkGoogle Scholar
  • Ibragimov M, Ibragimov R, Walden J (2015) Heavy-Tailed Distributions and Robustness in Economics and Finance, vol. 214 of Lecture Notes in Statistics (Springer, Berlin).CrossrefGoogle Scholar
  • Ibragimov R, Jaffee D, Walden J (2009) Non-diversification traps in markets for catastrophic risk. Rev. Financial Stud. 22:959–993.CrossrefGoogle Scholar
  • Ibragimov R, Jaffee D, Walden J (2011) Diversification disasters. J. Financial Econom. 99(2):333–348.CrossrefGoogle Scholar
  • Joag-Dev K, Proschan F (1983) Negative association of random variables with applications. Ann. Statist. 11(1):286–295.CrossrefGoogle Scholar
  • Kaas R, Goovaerts M, Tang Q (2004) Some useful counterexamples regarding comonotonicity. Belgian Actuarial Bull. 4(1):1–4.Google Scholar
  • Lehmann EL (1966) Some concepts of dependence. Ann. Math. Statist. 37(5):1137–1153.CrossrefGoogle Scholar
  • Levy H (1992) Stochastic dominance and expected utility: Survey and analysis. Management Sci. 38(4):555–593.LinkGoogle Scholar
  • Levy H (2016) Stochastic Dominance. Investment Decision Making Under Uncertainty, 3rd ed. (Springer, Berlin).CrossrefGoogle Scholar
  • Malinvaud E (1972) The allocation of individual risks in large markets. J. Econom. Theory 4(2):312–328.CrossrefGoogle Scholar
  • Marshall AW, Olkin I, Arnold B (2011) Inequalities: Theory of Majorization and Its Applications, 2nd ed. (Springer, Berlin).CrossrefGoogle Scholar
  • McNeil AJ, Frey R, Embrechts P (2015) Quantitative Risk Management: Concepts, Techniques and Tools, revised ed. (Princeton University Press, Princeton, NJ).Google Scholar
  • Müller A, Stoyan D (2002) Comparison Methods for Stochastic Models and Risks (Wiley, London).Google Scholar
  • Müller A, Scarsini M, Tsetlin I, Winkler RL (2017) Between first and second-order stochastic dominance. Management Sci. 63(9):2933–2947.LinkGoogle Scholar
  • Pickands J (1975) Statistical inference using extreme order statistics. Ann. Statist. 3:119–131.CrossrefGoogle Scholar
  • Proschan F (1965) Peakedness of distributions of convex combinations. Ann. Math. Statist. 36(6):1703–1706.CrossrefGoogle Scholar
  • Quirk JP, Saposnik R (1962) Admissibility and measurable utility functions. Rev. Econom. Stud. 29(2):140–146.CrossrefGoogle Scholar
  • Rothschild M, Stiglitz JE (1970) Increasing risk: I. A definition. J. Econom. Theory 2(3):225–243.CrossrefGoogle Scholar
  • Samuelson PA (1967) General proof that diversification pays. J. Financial Quant. Anal. 2(1):1–13.CrossrefGoogle Scholar
  • Schmidt U, Zank H (2008) Risk aversion in cumulative prospect theory. Management Sci. 54:208–216.LinkGoogle Scholar
  • Shaked M, Shanthikumar JG (2007) Stochastic Orders (Springer, Berlin).CrossrefGoogle Scholar
  • Shapiro C, Varian HR (1999) Information Rules: A Strategic Guide to the Network Economy (Harvard Business Press, Cambridge, MA).Google Scholar
  • Taleb N (2020) Statistical Consequences of Fat Tails (STEM Academic Press, New York).Google Scholar
  • Wang R, Zitikis R (2021) An axiomatic foundation for the expected shortfall. Management Sci. 67:1413–1429.LinkGoogle Scholar
  • Whitmore GA (1970) Third-degree stochastic dominance. Amer. Econom. Rev. 60(3):457–459.Google Scholar
  • Yaari ME (1987) The dual theory of choice under risk. Econometrica 55(1):95–115.CrossrefGoogle Scholar
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