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Martingale inequalities and deterministic counterparts


 
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1. Title Title of document Martingale inequalities and deterministic counterparts
 
2. Creator Author's name, affiliation, country Mathias Beiglböck; University of Vienna; Austria
 
2. Creator Author's name, affiliation, country Marcel Nutz; Columbia University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Martingale inequality; Concave envelope; Fixed point; Robust hedging; Tchakaloff's theorem
 
3. Subject Subject classification 60G42; 49L20
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF; FWF
 
7. Date (YYYY-MM-DD) 2014-10-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3270
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3270
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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