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The Azéma-Yor embedding in non-singular diffusions

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  • Pedersen, J. L.
  • Peskir, G.
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    Abstract

    Let (Xt)t[greater-or-equal, slanted]0 be a non-singular (not necessarily recurrent) diffusion on starting at zero, and let [nu] be a probability measure on Necessary and sufficient conditions are established for [nu] to admit the existence of a stopping time [tau]* of (Xt) solving the Skorokhod embedding problem, i.e. X[tau]* has the law [nu]. Furthermore, an explicit construction of [tau]* is carried out which reduces to the Azéma-Yor construction (Séminaire de Probabilités XIII, Lecture Notes in Mathematics, Vol. 721, Springer, Berlin, p. 90) when the process is a recurrent diffusion. In addition, this [tau]* is characterized uniquely to be a pointwise smallest possible embedding that stochastically maximizes (minimizes) the maximum (minimum) process of (Xt) up to the time of stopping.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 96 (2001)
    Issue (Month): 2 (December)
    Pages: 305-312

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    Handle: RePEc:eee:spapps:v:96:y:2001:i:2:p:305-312

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    Related research

    Keywords: The Skorokhod embedding problem Non-singular diffusion Non-recurrent Time-change Azema-Yor embedding Barycentre function Maximum/minimum process;

    References

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    1. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    2. Grandits, Peter & Falkner, Neil, 2000. "Embedding in Brownian motion with drift and the Azéma-Yor construction," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 249-254, February.
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    Cited by:
    1. 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.
    2. 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.
    3. Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2033-2048.

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