Multiperiod martingale transport

Marcel Nutz, Florian Stebegg and Xiaowei Tan

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1568-1615

Abstract: Consider a multiperiod optimal transport problem where distributions μ0,…,μn are prescribed and a transport corresponds to a scalar martingale X with marginals Xt∼μt. We introduce particular couplings called left-monotone transports; they are characterized equivalently by a no-crossing property of their support, as simultaneous optimizers for a class of bivariate transport cost functions with a Spence–Mirrlees property, and by an order-theoretic minimality property. Left-monotone transports are unique if μ0 is atomless, but not in general. In the one-period case n=1, these transports reduce to the Left-Curtain coupling of Beiglböck and Juillet. In the multiperiod case, the bivariate marginals for dates (0,t) are of Left-Curtain type, if and only if μ0,…,μn have a specific order property. The general analysis of the transport problem also gives rise to a strong duality result and a description of its polar sets. Finally, we study a variant where the intermediate marginals μ1,…,μn−1 are not prescribed.

Keywords: Optimal transport; Martingale coupling; Duality (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2019.05.010

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