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On multivalued martingales whose values may be unbounded: martingale selectors and mosco convergence

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  • Hess, Christian

Abstract

Using classical results on the projective limit of a sequence of subsets, we show the existence of martingale selectors for a multivalued martingale (and supermartingale) with closed values in a separable Banach space X. The existence of L1(X)-bounded or uniformly integrable martingale selectors is also discussed. At last, applications to the Mosco convergence of multivalued supermartingales and supermartingale integrands are provided.

Suggested Citation

  • Hess, Christian, 1991. "On multivalued martingales whose values may be unbounded: martingale selectors and mosco convergence," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 175-201, October.
    • Handle: RePEc:eee:jmvana:v:39:y:1991:i:1:p:175-201
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    Cited by:

    1. Jérôme Couvreux & Christian Hess, 1999. "A Lévy Type Martingale Convergence Theorem for Random Sets with Unbounded Values," Journal of Theoretical Probability, Springer, vol. 12(4), pages 933-969, October.
    2. Pedro Terán, 2016. "A Multivalued Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 29(2), pages 349-358, June.
    3. Katsiaryna Kaval & Ilya Molchanov, 2005. "Link-save trading and pricing of contingent claims," Finance 0511017, University Library of Munich, Germany.
    4. Kaval, K. & Molchanov, I., 2006. "Link-save trading," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 710-728, September.
    5. Ezzaki, Fatima & Tahri, Khalid, 2019. "Representation theorem of set valued regular martingale: Application to the convergence of set valued martingale," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.

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