E. N. Barron, P. Cardaliaguet, and R. Jensen, Conditional Essential Suprema with Applications, Applied Mathematics and Optimization, vol.48, issue.3, pp.229-253, 2003.
DOI : 10.1007/s00245-003-0776-4

B. Bensaid, J. P. Lesne, H. Pagès, and J. Scheinkman, DERIVATIVE ASSET PRICING WITH TRANSACTION COSTS, Mathematical Finance, vol.15, issue.4, pp.63-86, 1992.
DOI : 10.2307/2328113

L. Carassus, E. Gobet, and E. Temam, A Class of Financial Products and Models Where Super-replication Prices are Explicit, Stochastic Processes and Applications to Mathematical Finance, 2006.
DOI : 10.1142/9789812770448_0004

URL : https://hal.archives-ouvertes.fr/hal-00196279

L. Carassus and T. Vargiolu, Super-replication price: it can be ok, 2017.

A. S. Cherny, Pricing with Coherent Risk, Theory of Probability & Its Applications, vol.52, issue.3, pp.389-415
DOI : 10.1137/S0040585X97983158

E. C. Dalang, A. Morton, and W. Willinger, Equivalent martingale measures and no-arbitrage in stochastic securities market models, Stochastics and Stochastic Reports, vol.19, issue.2, pp.185-201, 1990.
DOI : 10.1017/S0001867800016360

F. Delbaen and W. Schachermayer, The Mathematics of Arbitrage, 2006.

H. Föllmer and D. Kramkov, Optional Decompositions under Constraints, Probability Theory and Related Fields, pp.1-25, 1997.

J. M. Harrison and D. M. Kreps, Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, vol.20, issue.3, pp.381-408, 1979.
DOI : 10.1016/0022-0531(79)90043-7

J. M. Harrison and S. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and their Applications, pp.215-260, 1981.
DOI : 10.1016/0304-4149(81)90026-0

C. Hess, Set-valued integration and set-valued probability theory: An overview, Handbook of Measure Theory, pp.617-673, 2002.

Y. Kabanov and M. Safarian, Markets with transaction costs. Mathematical Theory, 2009.
DOI : 10.1007/978-3-540-68121-2

URL : https://hal.archives-ouvertes.fr/hal-00488168

Y. Kabanov and E. Lépinette, Essential supremum with respect to a random partial order, Journal of Mathematical Economics, vol.49, issue.6, pp.478-487, 2013.
DOI : 10.1016/j.jmateco.2013.07.002

URL : https://hal.archives-ouvertes.fr/hal-00608856

D. Kreps, Arbitrage and equilibrium in economies with infinitely many commodities, Journal of Mathematical Economics, vol.8, issue.1, pp.15-35, 1981.
DOI : 10.1016/0304-4068(81)90010-0

E. Lépinette and I. Molchanov, Conditional cores and conditional convex hulls of random sets

E. Lépinette and T. Tran, Approximate Hedging in a Local Volatility Model with Proportional Transaction Costs, Applied Mathematical Finance, vol.342, issue.4, pp.313-341, 2014.
DOI : 10.1214/aoap/1060202836

G. N. Milstein, The Probability Approach to Numerical Solution of Nonlinear Parabolic Equations. Numerical methods for partial differential equations, pp.490-522, 2002.

R. T. Rockafellar, Convex analysis, 1972.
DOI : 10.1515/9781400873173

R. T. Rockafellar and R. J. Wets, Variational analysis, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1998.
DOI : 10.1007/978-3-642-02431-3