M. Akian, J. L. Menaldi, and A. Sulem, On an Investment-Consumption Model with Transaction Costs, SIAM Journal on Control and Optimization, vol.34, issue.1, pp.329-364, 1996.
DOI : 10.1137/S0363012993247159

M. Akian, P. Sequier, and A. Sulem, A finite horizon multidimensional portfolio selection problem with singular transactions, Proceedings of 1995 34th IEEE Conference on Decision and Control, pp.2193-2198, 1995.
DOI : 10.1109/CDC.1995.480528

A. Altarovici, J. Muhle-karbe, and H. M. Soner, Asymptotics for fixed transaction costs, preprint, 2013.

L. Ambrosio, Lecture Notes on Optimal Transport Problems, Lecture Notes in Mathematics, 2000.
DOI : 10.1007/978-3-540-39189-0_1

C. Atkinson and S. Mokkhavesa, Multi???asset portfolio optimization with transaction cost, Applied Mathematical Finance, vol.11, issue.2, pp.95-123, 2004.
DOI : 10.1080/13504860410001693496

M. Avellaneda, A. Lévy, and A. Parás, Pricing and hedging derivative securities in markets with uncertain volatilities, Applied Mathematical Finance, vol.7, issue.2, pp.73-88, 1995.
DOI : 10.2307/2330793

D. Baker, Martingales with specified marginals, pp.35-37, 2012.

G. Barles and H. M. Soner, Option pricing with transaction costs and a nonlinear Black-Scholes equation, Finance and Stochastics, vol.2, issue.4, pp.369-397, 1998.
DOI : 10.1007/s007800050046

M. Beiglböck, P. Henry-labordère, and F. Penkner, Model-independent Bounds for Option Prices: A Mass-Transport Approach, preprint arXiv:1106, Finance and Stochastics, vol.5929, 2013.

M. Beiglböck and N. Juillet, On a problem of optimal transport under marginal martin-gale constraints, preprint, 2012.

D. P. Bertsekas and S. E. Shreve, Stochastic Optimal Control. The Discrete-Time Case, 1978.

S. Biagini and M. Frittelli, Utility Maximisation in Incomplete Markets for Unbounded Processes, Finance and Stochastics, issue.4, pp.493-517, 2005.

S. Biagini and M. Frittelli, The supermartingale property of the optimal wealth process for general semimartingales, Finance and Stochastics, vol.4, issue.2, pp.253-266, 2007.
DOI : 10.1007/s00780-006-0026-0

S. Biagini, M. Frittelli, and M. Grasselli, INDIFFERENCE PRICE WITH GENERAL SEMIMARTINGALES, Mathematical Finance, vol.23, issue.3, pp.423-446, 2011.
DOI : 10.1111/j.1467-9965.2010.00443.x
URL : http://arxiv.org/abs/0905.4657

K. M. Bichteler, Stochastic integration and L p -theory of semimartingales Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment, Finance and Stochastics, to appear, The Annal of Probability, vol.9, issue.101 108, pp.19-89, 1981.

M. Bichuch, Asymptotic Analysis for Optimal Investment in Finite Time with Transaction Costs, SIAM Journal on Financial Mathematics, vol.3, issue.1, pp.433-458, 2012.
DOI : 10.1137/100808046

M. Bichuch and S. E. Shreve, Utility Maximization Trading Two Futures with Transaction Costs, SIAM Journal on Financial Mathematics, vol.4, issue.1, pp.26-85, 2013.
DOI : 10.1137/110853649
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.8802

P. Billingsley, Convergence of Probability Measures, Wiley Series in Probability and Statistics, 1999.
DOI : 10.1002/9780470316962

G. Bordigoni, A. Matoussi, and M. Schweizer, A stochastic control approach to a robust utility maximization problemStochastic analysis and applications, Abel Symp, pp.125-151, 2007.

B. Bouchard, Option pricing via utility maximization in the presence of transaction costs: an asymptotic analysis, pp.2000-00066707, 2000.

B. Bouchard, R. Elie, and C. Imbert, Optimal Control under Stochastic Target Constraints, SIAM Journal on Control and Optimization, vol.48, issue.5, pp.3501-3531, 2009.
DOI : 10.1137/090757629
URL : https://hal.archives-ouvertes.fr/hal-00373306

B. Bouchard, Y. M. Kabanov, and N. Touzi, Option pricing by large risk aversion utility under transaction costs, Decisions in Economics and Finance, pp.127-136, 2001.

B. Bouchard, L. Moreau, and M. Nutz, Stochastic target games with controlled loss, The Annals of Applied Probability, vol.24, issue.3, 2012.
DOI : 10.1214/13-AAP938
URL : https://hal.archives-ouvertes.fr/hal-00712713

B. Bouchard, L. Moreau, and H. M. Soner, Hedging under an expected loss constraint with small transaction costs, preprint, pp.16-96, 2013.

B. Bouchard and N. Touzi, Weak Dynamic Programming Principle for Viscosity Solutions, SIAM Journal on Control and Optimization, vol.49, issue.3, pp.948-962, 2011.
DOI : 10.1137/090752328
URL : https://hal.archives-ouvertes.fr/hal-00367355

D. T. Breeden and R. H. Litzenberger, Prices of State-Contingent Claims Implicit in Option Prices, The Journal of Business, vol.51, issue.4, p.621651, 1978.
DOI : 10.1086/296025

G. Carlier, Optimal Transportation and Economic Applications, Lecture Notes, 2012.

P. Carr and A. Chou, Breaking barriers, Risk, vol.109, pp.139-145, 1997.

X. Chen and M. Dai, Characterization of Optimal Strategy for Multi-Asset Investment and Consumption with Transaction Costs, SSRN Electronic Journal, 2013.
DOI : 10.2139/ssrn.2175413

G. M. Constantinides and M. J. Magill, Portfolio selection with transaction costs, J. Econ. Theory, vol.49, pp.33-83, 1976.

G. M. Constantinides and T. Zariphopoulou, Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences, Finance and Stochastics, vol.3, issue.3, pp.345-369, 1999.
DOI : 10.1007/s007800050066

G. M. Constantinides and T. Zariphopoulou, Bounds on Derivative Prices in an Intertemporal Setting with Proportional Transaction Costs and Multiple Securities, Mathematical Finance, vol.11, issue.3, pp.331-346, 2001.
DOI : 10.1111/1467-9965.00118

M. H. Davis and J. M. Clark, A Note on Super-Replicating Strategies, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.347, issue.1684, pp.485-494, 1684.
DOI : 10.1098/rsta.1994.0058

M. H. Davis, V. G. Panas, and T. Zariphopoulou, European Option Pricing with Transaction Costs, SIAM Journal on Control and Optimization, vol.31, issue.2, pp.470-493, 1993.
DOI : 10.1137/0331022

F. Delbaen, P. Grandits, T. Rheinländer, D. Samperi, M. Schweizer et al., Exponential Hedging and Entropic Penalties, Mathematical Finance, vol.23, issue.2, pp.99-123, 2001.
DOI : 10.1111/1467-9965.00093
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.552.9442

C. Dellacherie and P. A. Meyer, Probabilities and potential B, North Holland, 1982.

L. Denis and M. Kervarec, Utility functions and optimal investment in nondominated models, preprint, 2007.

L. Denis and C. Martini, A theoretical framework for the pricing of contingent claims in the presence of model uncertainty, The Annals of Applied Probability, vol.16, issue.2, pp.827-852, 2006.
DOI : 10.1214/105051606000000169

Y. Dolinsky and H. M. Soner, Martingale optimal transport and robust hedging in continuous time, Probability Theory and Related Fields, 2012.

B. Dupire, Pricing with a smile, Risk, vol.7, pp.18-20, 1994.

E. Karoui, N. Tan, and X. , Capacities, measurable selection and dynamic programming Part I: abstract framework, preprint, 2013.

E. Karoui, N. Tan, and X. , Capacities, measurable selection and dynamic programming Part II: application in stochastic control problems, preprint, 2013.

W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Applications of Mathematics, vol.25, 1986.

H. Föllmer, Calcul d'ito sans probabilites, Lecture Notes in Mathematics, vol.850, pp.9143-150, 1981.
DOI : 10.1007/BFb0088364

A. Galichon, P. Henry-labordère, and N. Touzi, A stochastic control approach to no-arbitrage bounds given marginals, with an application to Lookback options, Annals of Applied Probability, issue.7, pp.12-40, 2013.

S. Gerhold, J. Muhle-karbe, and W. Schachermayer, Asymptotics and duality for the Davis and Norman problem, Stochastics An International Journal of Probability and Stochastic Processes, vol.4, issue.3, pp.625-641, 2012.
DOI : 10.1111/1467-9965.00034

I. Gilboa and D. Schmeidler, Maxmin expected utility with non-unique prior, Journal of Mathematical Economics, vol.18, issue.2, pp.141-153, 1989.
DOI : 10.1016/0304-4068(89)90018-9
URL : https://hal.archives-ouvertes.fr/hal-00753237

J. Goodman and D. N. Ostrov, Balancing Small Transaction Costs with Loss of Optimal Allocation in Dynamic Stock Trading Strategies, SIAM Journal on Applied Mathematics, vol.70, issue.6, pp.1977-1998, 2010.
DOI : 10.1137/07070334X

V. Henderson and D. Hobson, An explicit solution for an optimal stopping/optimal control problem which models an asset sale, The Annals of Applied Probability, vol.18, issue.5, pp.1681-1705, 2008.
DOI : 10.1214/07-AAP511

P. Henry-labordère, J. Oblój, P. Spoida, and N. Touzi, Maximum maximum of martingales given finitely-many intermediate marginals, preprint, pp.40-43, 2012.

P. Henry-labordère and N. Touzi, An explicit Version of the Brenier Theorem in Martingale Optimal Transportation, 2013.

F. Hirsch, C. Profeta, B. Roynette, and M. Yor, Constructing self-similar martingales via two Skorokhod embeddings, Séminaire de Probabilités XLIII, Lecture Notes in Mathematics, pp.451-503, 2011.

F. Hirsch, C. Profeta, B. Roynette, and M. Yor, Peacocks and Associated Martingales , with Explicit Constructions, 2011.
DOI : 10.1007/978-88-470-1908-9
URL : https://hal.archives-ouvertes.fr/hal-00657769

F. Hirsch and B. Roynette, A new proof of Kellerer???s theorem, ESAIM: Probability and Statistics, vol.16, pp.48-60, 2012.
DOI : 10.1051/ps/2011164

D. Hobson, The skorokhod embedding problem and model-independent bounds for option prices, Paris-Princeton Lectures on, Mathematical Finance, Lecture Notes in Mathematics

D. Hobson and J. Pedersen, The minimum maximum of a continuous martingale with given initial and terminal laws, Annals of probability, pp.978-999, 2002.

S. Hodges and A. Neuberger, Option replication of contingent claims under transaction costs, Review of Futures Markets, pp.222-239, 1989.

K. Jane?ek and S. E. Shreve, Asymptotic analysis for optimal investment and consumption with transaction costs, Finance and Stochastics, vol.8, issue.2, pp.181-206, 2004.
DOI : 10.1007/s00780-003-0113-4

K. Jane?ek and S. E. Shreve, Futures trading with transaction costs, Ilinois Journal of Mathematics, vol.54, issue.4, pp.1239-1284, 2010.

Y. M. Kabanov and M. Safarian, Markets with transaction costs, 2009.
DOI : 10.1007/978-3-540-68121-2
URL : https://hal.archives-ouvertes.fr/hal-00488168

Y. Kabanov and C. Stricker, On the optimal portfolio for the exponential utility maximization: remarks to the six-author paper, Mathematical Finance, vol.3, issue.2, pp.125-134, 2002.
DOI : 10.1214/aoap/1029962818

J. Kallsen and J. Muhle-karbe, Option pricing and hedging with small transaction costs, Mathematical Finance, to appear, vol.111, p.16, 2012.

J. Kallsen and J. Muhle-karbe, The general structure of optimal investment and consumption with small transaction costs, preprint, p.16, 2013.

R. Karandikar, On pathwise stochastic integration, Stochastic Processes and Their Applications, pp.11-18, 1995.

N. Kazi-tani, D. Possamaï, and C. Zhou, Second order BSDEs with jumps, part II: existence and applications, preprint, p.44, 2012.

H. G. Kellerer, Markov-Komposition und eine Anwendung auf Martingale, Mathematische Annalen, vol.36, issue.3, pp.99-122, 1972.
DOI : 10.1007/BF01432281
URL : http://www.digizeitschriften.de/download/PPN235181684_0198/PPN235181684_0198___log19.pdf

S. Levental and A. V. Skorohod, On the possibility of hedging options in the presence of transaction costs, The Annals of Applied Probability, vol.7, issue.2, pp.410-443, 1997.
DOI : 10.1214/aoap/1034625338

T. J. Lyons, Uncertain volatility and the risk-free synthesis of derivatives, Applied Mathematical Finance, vol.20, issue.2, pp.117-133, 1995.
DOI : 10.1002/cpa.3160450103

A. Matoussi, D. Possamaï, and C. Zhou, Robust utility maximization in nondominated models with 2BSDEs, Mathematical Finance, 2013.

R. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, vol.3, issue.4, pp.373-413, 1971.
DOI : 10.1016/0022-0531(71)90038-X

L. Moreau, J. Muhle-karbe, and H. M. Soner, Portfolio choice with small market impact, preprint, 2013.

P. Morters and Y. Peres, Brownian motion, Cambridge Series in Statistical and Probabilistic Mathematics

A. Neufeld and M. Nutz, Superreplication under volatility uncertainty for measurable claims, Electronic Journal of Probability, vol.18, issue.0, pp.1-14, 2013.
DOI : 10.1214/EJP.v18-2358

J. Neveu, Discrete-Parameter Martingales, North-Holland, 1975.

M. Nutz, Pathwise construction of stochastic integrals, Electronic Communications in Probability, vol.17, issue.0, pp.1-7, 2012.
DOI : 10.1214/ECP.v17-2099

M. Nutz and R. Van-handel, Constructing sublinear expectations on path space, preprint, Stochastic Processes and their Applications, pp.3100-3121, 2012.

T. Pham and J. Zhang, Two Person Zero-sum Game in Weak Formulation and Path Dependent Bellman-Isaacs Equation, preprint, 2012.

S. R. Pliska, A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios, Mathematics of Operations Research, vol.11, issue.2, pp.371-382, 1986.
DOI : 10.1287/moor.11.2.371

D. Possamaï, H. M. Soner, and N. Touzi, Large liquidity expansions of superhedging costs, Asymptotic Analysis, vol.79, issue.12, pp.45-64, 2012.

D. Possamaï, H. M. Soner, and N. Touzi, Homogenization and asymptotics for small transaction costs: the multidimensional case, preprint, arXiv:1212.6275, pp.16-118, 2013.

P. Protter, Stochastic integration and differential equations, 2004.

L. C. Rogers, Equivalent martingale measures and no-arbitrage, Stochastics and Stochastic Reports, vol.26, issue.1-2, pp.41-49, 1994.
DOI : 10.1080/17442509408833943