Electronic Journal of Probability

Martingale inequalities and deterministic counterparts

Mathias Beiglböck and 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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065737

Digital Object Identifier
doi:10.1214/EJP.v19-3270

Mathematical Reviews number (MathSciNet)
MR3272328

Zentralblatt MATH identifier
1307.60044

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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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