Kellerer’s Theorem Revisited

  • Francis HirschEmail author
  • Bernard Roynette
  • Marc Yor
Part of the Fields Institute Communications book series (FIC, volume 76)


Kellerer’s theorem asserts the existence of a Markov martingale with given marginals, assumed to increase in the convex order. It is revisited here, in the light of previous papers by Hirsch-Roynette and by G. Lowther.


Probability Measure Call Function Markov Property Easy Consequence Step Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Dellacherie, C., Meyer, P.-A.: Probabilités et potentiel, Chapitres V à VIII, Théorie des martingales, Hermann (1980)zbMATHGoogle Scholar
  2. 2.
    Derman, E., Kani, I.: Riding on a smile. Risk 7, 32–39 (1994)Google Scholar
  3. 3.
    Dupire, B.: Pricing with a smile. Risk Mag. 7, 18–20 (1994)Google Scholar
  4. 4.
    Hirsch, F., Roynette, B.: A new proof of Kellerer’s theorem. ESAIM: PS 16, 48–60 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Hirsch, F., Profeta, C., Roynette, B., Yor, M.: Peacocks and Associated Martingales, with Explicit Constructions. Bocconi & Springer Series, vol. 3. Springer, Milan (2011)Google Scholar
  6. 6.
    Kellerer, H.G.: Markov-Komposition und eine Anwendung auf Martingale. Math. Ann. 198, 99–122 (1972)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Lowther, G.: Properties of expectations of functions of martingale diffusions. (2008)
  8. 8.
    Lowther, G.: Fitting martingales to given marginals. (2008)
  9. 9.
    Lowther, G.: Limits of one-dimensional diffusions. Ann. Proba. 37(1), 78–106 (2009)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Laboratoire d’Analyse et ProbabilitésUniversité d’Évry-Val d’EssonneEvry CedexFrance
  2. 2.Institut Elie CartanUniversité Henri PoincaréVandœuvre-lès-Nancy CedexFrance
  3. 3.Laboratoire de Probabilités et Modèles AléatoiresUniversité Paris VI et VIIParis Cedex 05France
  4. 4.Institut Universitaire de FranceParisFrance

Personalised recommendations