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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.

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  • 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. 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.
    3. 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.
    4. 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.
    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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