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Couplings for processes with independent increments

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  • Criens, David

Abstract

Strassen’s theorem states that the usual stochastic order of two processes is equivalent to the existence of a pathwise ordered coupling. In the case of processes with independent increments, we construct explicit pathwise ordered couplings under suitable conditions on the characteristics of the processes. To formalize the couplings we use independent decompositions, a redistribution mechanism for jumps and Itô’s map, which relates general Lévy measures to a reference Lévy measure.

Suggested Citation

  • Criens, David, 2019. "Couplings for processes with independent increments," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 161-167.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:161-167
    DOI: 10.1016/j.spl.2018.11.016
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    1. Criens, David, 2018. "A note on the monotone stochastic order for processes with independent increments," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 127-131.
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    Cited by:

    1. Frank Bosserhoff & Mitja Stadje, 2019. "Robustness of Delta Hedging in a Jump-Diffusion Model," Papers 1910.08946, arXiv.org, revised Apr 2022.

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