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The increasing supermartingale coupling, introduced by Nutz and Stebegg(Canonical supermartingale couplings, Annals of Probability, 46(6):3351--3398,2018) is an extreme point of the set of `supermartingale' couplings between tworeal probability measures in convex-decreasing order. In the present paper weprovide an explicit construction of a triple of functions, on the graph ofwhich the increasing supermartingale coupling concentrates. In particular, weshow that the increasing supermartingale coupling can be identified with theleft-curtain martingale coupling and the antitone coupling to the left and tothe right of a uniquely determined regime-switching point, respectively.  Our construction is based on the concept of the shadow measure. We show howto determine the potential of the shadow measure associated to asupermartingale, extending the recent results of Beiglb\"{o}ck et al. (Thepotential of the shadow measure, Electron. Commun. Probab., 27, paper no. 16,1--12, 2022) obtained in the martingale setting.

A potential-based construction of the increasing supermartingale coupling