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MRL order, log-concavity and an application to peacocks

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  • Bogso, Antoine Marie

Abstract

We provide an equivalent log-concavity condition to the mean residual life (MRL) ordering for real-valued processes. This result, combined with classical properties of total positivity of order 2, allows to exhibit new families of integrable processes which increase in the MRL order (MRL processes). Note that MRL processes with constant mean are peacocks to which the Azéma–Yor (Skorokhod embedding) algorithm yields an explicit associated martingale.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1282-1306
    DOI: 10.1016/j.spa.2014.10.015
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    References listed on IDEAS

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    1. Daduna, Hans & Szekli, Ryszard, 1996. "A queueing theoretical proof of increasing property of Polya frequency functions," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 233-242, February.
    2. Carr, Peter & Ewald, Christian-Oliver & Xiao, Yajun, 2008. "On the qualitative effect of volatility and duration on prices of Asian options," Finance Research Letters, Elsevier, vol. 5(3), pages 162-171, September.
    3. Lim, Adrian P.C. & Yen, Ju-Yi & Yor, Marc, 2013. "Some examples of Skorokhod embeddings obtained from the Azéma–Yor algorithm," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 329-346.
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    Cited by:

    1. Antoine-Marie Bogso, 2020. "Mean Residual Life Processes and Associated Submartingales," Journal of Theoretical Probability, Springer, vol. 33(1), pages 36-64, March.
    2. Bogso, Antoine-Marie & Takam Soh, Patrice, 2017. "Weak decreasing stochastic order," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 49-58.

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