Martingale Inequalities, Optimal Martingale Transport, and Robust Superhedging*
In the recent literature, martingale inequalities have been emphasized to be induced by pathwise inequalities independently of any reference probability measure on the paths space. This feature is closely related to the problem of robust hedging in financial mathematics...
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EDP Sciences
2014-09-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | http://dx.doi.org/10.1051/proc/201445004 |
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doaj-c66e2b43bc82473aa5552263af4bf6382021-07-15T14:07:21ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592014-09-0145324710.1051/proc/201445004proc144504Martingale Inequalities, Optimal Martingale Transport, and Robust Superhedging*Touzi Nizar0Ecole Polytechnique Paris, Centre de Mathématiques AppliquéesIn the recent literature, martingale inequalities have been emphasized to be induced by pathwise inequalities independently of any reference probability measure on the paths space. This feature is closely related to the problem of robust hedging in financial mathematics, which was originally addressed in some specific cases by means of the Skorohod embedding problem. The martingale optimal transport problem provides a systematic framework for the robust hedging problem and, therefore, allows to derive sharp martingale inequalities. We illustrate this methodology by deriving the sharpest possible control of the running maximum of a martingale by means of a finite number of marginals.http://dx.doi.org/10.1051/proc/201445004 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Touzi Nizar |
| spellingShingle |
Touzi Nizar Martingale Inequalities, Optimal Martingale Transport, and Robust Superhedging* ESAIM: Proceedings and Surveys |
| author_facet |
Touzi Nizar |
| author_sort |
Touzi Nizar |
| title |
Martingale Inequalities, Optimal Martingale Transport, and
Robust Superhedging* |
| title_short |
Martingale Inequalities, Optimal Martingale Transport, and
Robust Superhedging* |
| title_full |
Martingale Inequalities, Optimal Martingale Transport, and
Robust Superhedging* |
| title_fullStr |
Martingale Inequalities, Optimal Martingale Transport, and
Robust Superhedging* |
| title_full_unstemmed |
Martingale Inequalities, Optimal Martingale Transport, and
Robust Superhedging* |
| title_sort |
martingale inequalities, optimal martingale transport, and
robust superhedging* |
| publisher |
EDP Sciences |
| series |
ESAIM: Proceedings and Surveys |
| issn |
2267-3059 |
| publishDate |
2014-09-01 |
| description |
In the recent literature, martingale inequalities have been emphasized to be induced by
pathwise inequalities independently of any reference probability measure on the paths
space. This feature is closely related to the problem of robust hedging in financial
mathematics, which was originally addressed in some specific cases by means of the
Skorohod embedding problem. The martingale optimal transport problem provides a systematic
framework for the robust hedging problem and, therefore, allows to derive sharp martingale
inequalities. We illustrate this methodology by deriving the sharpest possible control of
the running maximum of a martingale by means of a finite number of marginals. |
| url |
http://dx.doi.org/10.1051/proc/201445004 |
| work_keys_str_mv |
AT touzinizar martingaleinequalitiesoptimalmartingaletransportandrobustsuperhedging |
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