Electronic Journal of Probability

Martingale inequalities and deterministic counterparts

Mathias Beiglböck and Marcel Nutz

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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.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 95, 15 pp.

Accepted: 16 October 2014
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G42: Martingales with discrete parameter
Secondary: 49L20: Dynamic programming method

Martingale inequality Concave envelope Fixed point Robust hedging Tchakaloff's theorem

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Beiglböck, Mathias; Nutz, Marcel. Martingale inequalities and deterministic counterparts. Electron. J. Probab. 19 (2014), paper no. 95, 15 pp. doi:10.1214/EJP.v19-3270. https://projecteuclid.org/euclid.ejp/1465065737

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