Document Zbl 1307.60044

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Martingale inequalities and deterministic counterparts. (English) Zbl 1307.60044

Electron. J. Probab. 19, Paper No. 95, 15 p. (2014).

Summary: 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.

Cited in 21 Documents

MSC:

60G42	Martingales with discrete parameter
91G80	Financial applications of other theories

Keywords:

martingale inequality; concave envelope; fixed point; robust hedging

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