Martingale Inequalities and Deterministic Counterparts

Mathias Beiglböck; Marcel Nutz

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arXiv · 1401.4698

Martingale Inequalities and Deterministic Counterparts

Mathias Beiglböck·Marcel Nutz

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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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Mathias Beiglböck, Marcel Nutz. 2014-10-18. Martingale Inequalities and Deterministic Counterparts. https://arxiv.org/abs/1401.4698

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