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A Characterization of Probabilities with Full Support and the Laplace Method

Author

Listed:
  • Simone Cerreia-Vioglio

    (Bocconi University)

  • Fabio Maccheroni

    (Bocconi University)

  • Massimo Marinacci

    (Bocconi University)

Abstract

We show that a probability measure on a metric space has full support, if, and only if, the set of all probability measures, that are absolutely continuous with respect to it, is dense in the set of all Borel probability measures. We illustrate the result through a general version of Laplace’s method, which in turn leads to general stochastic convergence to global maxima.

Suggested Citation

  • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2019. "A Characterization of Probabilities with Full Support and the Laplace Method," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 470-478, May.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:2:d:10.1007_s10957-018-01459-7
    DOI: 10.1007/s10957-018-01459-7
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    References listed on IDEAS

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    1. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    2. Martin Pincus, 1970. "Letter to the Editor—A Monte Carlo Method for the Approximate Solution of Certain Types of Constrained Optimization Problems," Operations Research, INFORMS, vol. 18(6), pages 1225-1228, December.
    3. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2016. "Universal arbitrage aggregator in discrete-time markets under uncertainty," Finance and Stochastics, Springer, vol. 20(1), pages 1-50, January.
    4. Martin Pincus, 1968. "Letter to the Editor—-A Closed Form Solution of Certain Programming Problems," Operations Research, INFORMS, vol. 16(3), pages 690-694, June.
    5. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, October.
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    Cited by:

    1. Simone Cerreia-Vioglio & Roberto Corrao & Giacomo Lanzani, 2020. "Robust Opinion Aggregation and its Dynamics," Working Papers 662, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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