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2014 Martingale inequalities and deterministic counterparts
Mathias Beiglböck, Marcel Nutz
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Electron. J. Probab. 19: 1-15 (2014). DOI: 10.1214/EJP.v19-3270

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. "Martingale inequalities and deterministic counterparts." Electron. J. Probab. 19 1 - 15, 2014. https://doi.org/10.1214/EJP.v19-3270

Information

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

zbMATH: 1307.60044
MathSciNet: MR3272328
Digital Object Identifier: 10.1214/EJP.v19-3270

Subjects:
Primary: 60G42
Secondary: 49L20

Keywords: Concave envelope , fixed point , martingale inequality , robust hedging , Tchakaloff's theorem

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