Martingale inequalities and deterministic counterparts

Mathias Beiglböck (University of Vienna)
Marcel Nutz (Columbia University)

Abstract


We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the martingale inequality is determined by a fixed point of a simple nonlinear operator involving a concave envelope. Our results yield an explanation for certain inequalities that arise in mathematical finance in the context of robust hedging.

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Pages: 1-15

Publication Date: October 16, 2014

DOI: 10.1214/EJP.v19-3270

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