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Quelques inégalités avec le temps local en zero du mouvement Brownien

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  • Vallois, P.

Abstract

Assume [phi] is a convex fonction, L is the local time at 0 of a Brownian motion B, started at 0 and [mu] is the set of good Brownian stopping times, embedding a fixed law [mu] on . We show that the maximum (resp. minimum) of E([phi](LT)), where belongs to [mu], is reached for an explicit stopping time. We compute 'best' constants in some inequalities involving LT and BT. We also give some new inequalities with LT and LT/B*T.

Suggested Citation

  • Vallois, P., 1992. "Quelques inégalités avec le temps local en zero du mouvement Brownien," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 117-155, May.
    • Handle: RePEc:eee:spapps:v:41:y:1992:i:1:p:117-155
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    Cited by:

    1. Bayraktar, Erhan & Zhang, Xin, 2021. "Embedding of Walsh Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 1-28.
    2. Julien Claisse & Gaoyue Guo & Pierre Henry-Labordere, 2015. "Some Results on Skorokhod Embedding and Robust Hedging with Local Time," Papers 1511.07230, arXiv.org, revised Oct 2017.
    3. Cox, A. M. G. & Hobson, D. G., 2004. "An optimal Skorokhod embedding for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 17-39, May.
    4. Julien Claisse & Gaoyue Guo & Pierre Henry-Labordère, 2018. "Some Results on Skorokhod Embedding and Robust Hedging with Local Time," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 569-597, November.
    5. Oblój, Jan, 2007. "An explicit solution to the Skorokhod embedding problem for functionals of excursions of Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 117(4), pages 409-431, April.

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