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Weak decreasing stochastic order

Author

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  • Bogso, Antoine-Marie
  • Takam Soh, Patrice

Abstract

We introduce the notion of weak decreasing stochastic (WDS) ordering for real-valued processes with negative means, which, to our knowledge, has not been studied before. Thanks to Madan–Yor’s argument, it follows that the WDS ordering is a necessary and sufficient condition for a family of integrable probability measures with negative mean to be embeddable in a standard Brownian motion by the Cox and Hobson extension of the Azéma–Yor algorithm. The resulting process is a supermartingale and if, in addition, the measures have densities, this supermartingale is Markovian. Then the Cox–Hobson algorithm provides a special solution of Kellerer’s theorem relying on the stronger hypothesis of WDS order.

Suggested Citation

  • Bogso, Antoine-Marie & Takam Soh, Patrice, 2017. "Weak decreasing stochastic order," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 49-58.
    • Handle: RePEc:eee:stapro:v:126:y:2017:i:c:p:49-58
    DOI: 10.1016/j.spl.2017.02.020
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    References listed on IDEAS

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    1. Bogso, Antoine Marie, 2015. "MRL order, log-concavity and an application to peacocks," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1282-1306.
    2. Ewald, Christian-Oliver & Yor, Marc, 2015. "On increasing risk, inequality and poverty measures: Peacocks, lyrebirds and exotic options," Journal of Economic Dynamics and Control, Elsevier, vol. 59(C), pages 22-36.
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    Cited by:

    1. Liu, Yating & Pagès, Gilles, 2022. "Monotone convex order for the McKean–Vlasov processes," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 312-338.

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