Weak Closedness of Monotone Sets of Lotteries and Robust Representation of Risk Preferences

  • Patrick Cheridito
  • Samuel Drapeau
  • Michael Kupper
Part of the EAA Series book series (EAAS)


We prove a closedness result for sets of lotteries that are monotone with respect to first-order stochastic dominance and show how it can be applied to obtain robust representations of risk preferences on lotteries with compact support.


Risk preferences Robust representations Lotteries with compact support Monotonicity 



P. Cheridito was supported in part by NSF Grant DMS-0642361. S. Drapeau financial support from MATHEON project E.11 is gratefully acknowledged.


  1. Artzner, P., Delbaen, F., Eber, J. M., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203–228. MathSciNetzbMATHCrossRefGoogle Scholar
  2. Cerreia-Vioglio, S. (2009). Maxmin expected utility on a subjective state space: convex preferences under risk (Preprint). Google Scholar
  3. Cheridito, P., & Li, T. (2008). Dual characterization of properties of risk measures on Orlicz hearts. Mathematics and Financial Economics, 2(1), 29–55. MathSciNetzbMATHCrossRefGoogle Scholar
  4. Cheridito, P., & Li, T. (2009). Monetary risk measures on maximal subspaces of Orlicz classes. Mathematical Finance, 19(2), 189–214. MathSciNetzbMATHCrossRefGoogle Scholar
  5. Delbaen, F., Drapeau, S., & Kupper, M. (2011). A von Neumann–Morgenstern representation result without weak continuity assumption. Journal of Mathematical Economics, 47, 401–408. MathSciNetzbMATHCrossRefGoogle Scholar
  6. Drapeau, S., & Kupper, M. (2010, forthcoming). Risk preferences and their robust representation. Mathematics of Operations Research. Google Scholar
  7. Fishburn, P. C. (1982). The foundations of expected utility. Dordrecht: D. Reidel Publishing. zbMATHGoogle Scholar
  8. Föllmer, H., & Schied, A. (2004). de Gruyter studies in mathematics. Stochastic finance—an introduction in discrete time (2nd ed.). Berlin: Walter de Gruyter. zbMATHCrossRefGoogle Scholar
  9. von Neumann, J., & Morgenstern, O. (1947). Theory of games and economics behavior (2nd ed.). Princeton: Princeton University Press. Google Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Patrick Cheridito
    • 1
  • Samuel Drapeau
    • 2
  • Michael Kupper
    • 2
  1. 1.Princeton UniversityPrincetonUSA
  2. 2.Humboldt University BerlinBerlinGermany

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