MODEL-FREE SUPERHEDGING DUALITY

被引:32
作者
Burzoni, Matte [1 ]
Frittelli, Marco [2 ]
Maggis, Marco [2 ]
机构
[1] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland
[2] Univ Milan, Dept Math, Via C Saldini 50, I-20122 Milan, Italy
关键词
Superhedging theorem; model independent market; model uncertainty; robust duality; finite support martingale measure; analytic sets; ARBITRAGE; MARTINGALE;
D O I
10.1214/16-AAP1235
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In a model-free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semistatic strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path omega is an element of Omega, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.
引用
收藏
页码:1452 / 1477
页数:26
相关论文
共 23 条
[1]   A MODEL-FREE VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING AND THE SUPER-REPLICATION THEOREM [J].
Acciaio, B. ;
Beiglboeck, M. ;
Penkner, F. ;
Schachermayer, W. .
MATHEMATICAL FINANCE, 2016, 26 (02) :233-251
[2]  
Aliprantis CD., 2006, INFINITE DIMENSIONAL
[3]  
[Anonymous], ROBUST PRICING HEDGI
[4]  
[Anonymous], FINANCE STOCH
[5]  
[Anonymous], CRM MONOGRAPH SERIES
[6]   Model-independent bounds for option prices-a mass transport approach [J].
Beiglboeck, Mathias ;
Henry-Labordere, Pierre ;
Penkner, Friedrich .
FINANCE AND STOCHASTICS, 2013, 17 (03) :477-501
[7]  
Bertsekas D., 1978, STOCHASTIC OPTIMAL C
[8]   ARBITRAGE AND DUALITY IN NONDOMINATED DISCRETE-TIME MODELS [J].
Bouchard, Bruno ;
Nutz, Marcel .
ANNALS OF APPLIED PROBABILITY, 2015, 25 (02) :823-859
[9]   Robust hedging of barrier options [J].
Brown, H ;
Hobson, D ;
Rogers, LCG .
MATHEMATICAL FINANCE, 2001, 11 (03) :285-314
[10]   Universal arbitrage aggregator in discrete-time markets under uncertainty [J].
Burzoni, Matteo ;
Frittelli, Marco ;
Maggis, Marco .
FINANCE AND STOCHASTICS, 2016, 20 (01) :1-50