M. Akian, J. 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

O. Alvarez and A. Tourin, Viscosity solutions of nonlinear integrodifferential equations. Annales de l'Institut Henri Poincaré, Analyse non linéaire, pp.293-317, 1996.

M. Arisawa, A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations. Annales de l'Institut Henri Poincare/Analyse non lineaire, pp.695-711, 2006.

M. Arisawa, A remark on the definitions of viscosity solutions for the integro-differential equations with L??vy operators, Journal de Math??matiques Pures et Appliqu??es, vol.89, issue.6, 2008.
DOI : 10.1016/j.matpur.2008.02.005

J. Aubin and S. Wilson, Optima and equilibria: an introduction to nonlinear analysis, 1993.

M. Bardi and I. Capuzzo-dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, 1997.
DOI : 10.1007/978-0-8176-4755-1

G. Barles, E. Chasseigne, and C. Imbert, On the Dirichlet problem for second-order elliptic integro-differential equations, Indiana University Mathematics Journal, vol.57, issue.1, pp.213-246, 2008.
DOI : 10.1512/iumj.2008.57.3315

URL : https://hal.archives-ouvertes.fr/hal-00150151

G. Barles and C. Imbert, Second-order elliptic integro-differential equations: viscosity solutions' theory revisited. Annales de l'Institut Henri Poincare/Analyse non lineaire, pp.567-585, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00130169

G. Barles and H. 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

F. Benth, K. Karlsen, and K. Reikvam, Optimal portfolio management rules in a non-Gaussian market with durability and intertemporal substitution, Finance and Stochastics, vol.5, issue.4, pp.447-467, 2001.
DOI : 10.1007/s007800000032

F. Benth, K. Karlsen, and K. Reikvam, Portfolio optimization in a Levy market with intertemporal substitution and transaction costs, Stochastics An International Journal of Probability and Stochastic Processes, vol.74, issue.3, pp.517-569, 2002.
DOI : 10.1080/1045112021000037382

B. Bouchard, No-arbitrage in Discrete-time Markets with Proportional Transaction Costs and General Information structure, Finance and Stochastics, vol.14, issue.3, pp.276-297, 2006.
DOI : 10.1007/s00780-006-0002-8

URL : https://hal.archives-ouvertes.fr/hal-00003764

B. Bouchard and J. F. Chassagneux, Representation of continuous linear forms on the set of ladlag processes and the pricing of american claims under proportional costs, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00270030

B. Bouchard and E. Temam, On the Hedging of American Options in Discrete Time with Proportional Transaction Costs, Electronic Journal of Probability, vol.10, issue.0, pp.746-760, 2005.
DOI : 10.1214/EJP.v10-266

URL : https://hal.archives-ouvertes.fr/hal-00002983

B. Bouchard and N. Touzi, Weak Dynamic Programming Principle for Viscosity Solutions, SIAM Journal on Control and Optimization, vol.49, issue.3, 2009.
DOI : 10.1137/090752328

URL : https://hal.archives-ouvertes.fr/hal-00367355

L. Campi and W. Schachermayer, A super-replication theorem in Kabanov???s model of transaction costs, Finance and Stochastics, vol.35, issue.4, pp.579-596, 2006.
DOI : 10.1007/s00780-006-0022-4

P. Chalasani and S. Jha, Randomized Stopping Times and American Option Pricing with Transaction Costs, Mathematical Finance, vol.11, issue.1, pp.33-77, 2001.
DOI : 10.1111/1467-9965.00107

M. Crandall, H. Ishii, and P. Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Amer. Math. Soc, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

J. Cvitani´ccvitani´c, I. Karatzas, R. Dalang, A. Morton, and W. Willinger, Hedging and portfolio optimization under transaction costs: a martingale approach Equivalent martingale measures and no-arbitrage in stochastic securities market models, Math. Finance Stochastics and stochastics reports, vol.620, issue.22, pp.133-165, 1990.

M. Davis and A. Norman, Portfolio Selection with Transaction Costs, Mathematics of Operations Research, vol.15, issue.4, pp.676-713, 1990.
DOI : 10.1287/moor.15.4.676

D. Devallì-ere, Y. Kabanov, and C. Stricker, No-arbitrage criteria for financial markets with transaction costs and incomplete information, Finance and Stochastics, vol.14, issue.2, pp.237-251, 2007.
DOI : 10.1007/s00780-006-0029-x

D. Devallì-ere, E. Denis, and Y. Kabanov, Hedging of American options under transaction costs, Finance and Stochastics, vol.105, issue.1, pp.105-119, 2009.
DOI : 10.1007/s00780-008-0076-6

C. Dellacherie and P. Meyer, Probabilités et potentiel. Hermann, Paris, 1975. Chapitres I ` a IV, ´ Editionentì erement refondue, Publications de l, 1372.

P. G. Grigoriev, On low dimensional case in the fundamental asset pricing theorem with transaction costs, Statistics & Decisions, vol.23, issue.1/2005, pp.33-48, 2005.
DOI : 10.1524/stnd.2005.23.1.33

J. Jacod and A. Shiryaev, Limit theorems for stochastic processes, A Series of Comprehensive Studies in Mathematics, vol.288, 1987.
DOI : 10.1007/978-3-662-02514-7

J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1987.
DOI : 10.1007/978-3-662-02514-7

K. Jane?ek and S. 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

E. Jouini and H. Kallal, Martingales and Arbitrage in Securities Markets with Transaction Costs, Journal of Economic Theory, vol.66, issue.1, pp.178-197, 1995.
DOI : 10.1006/jeth.1995.1037

Y. Kabanov, Hedging and liquidation under transaction costs in currency markets, Finance and Stochastics, vol.3, issue.2, pp.237-248, 1999.
DOI : 10.1007/s007800050061

Y. Kabanov and C. Klüppelberg, A geometric approach to portfolio optimization in models with transaction costs, Finance and Stochastics, vol.8, issue.2, pp.207-227, 2004.
DOI : 10.1007/s00780-003-0114-3

Y. Kabanov, M. Rásonyi, and C. Stricker, On the closedness of sums of convex cones in $L^0$ and the robust no-arbitrage property, Finance and Stochastics, vol.7, issue.3, pp.403-411, 2003.
DOI : 10.1007/s007800200089

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 C. Stricker, A teacher???s note on no-arbitrage criteria, Séminaire de Probabilités, XXXV, pp.149-152, 2001.
DOI : 10.1007/978-3-540-44671-2_9

Y. Kabanov and C. Stricker, The Dalang???Morton???Willinger Theorem Under Delayed and Restricted Information, memoriam Paul-André Meyer: Séminaire de Probabilités XXXIX, pp.209-213, 2006.
DOI : 10.1007/978-3-540-35513-7_16

URL : https://hal.archives-ouvertes.fr/hal-00488086

Y. M. Kabanov, Arbitrage theory In Option pricing, interest rates and risk management, Handb, Math. Finance, pp.3-42, 2001.

Y. M. Kabanov and G. Last, Hedging under Transaction Costs in Currency Markets: a Continuous-Time Model, Mathematical Finance, vol.5, issue.1, pp.63-70, 2002.
DOI : 10.1007/s001860050099

Y. M. Kabanov and C. Stricker, The Harrison???Pliska arbitrage pricing theorem under transaction costs, Journal of Mathematical Economics, vol.35, issue.2, pp.185-196, 2001.
DOI : 10.1016/S0304-4068(00)00064-1

Y. M. Kabanov and C. Stricker, Hedging of Contingent Claims under Transaction Costs, Advances in finance and stochastics, pp.125-136, 2002.
DOI : 10.1007/978-3-662-04790-3_7

D. O. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets. Probab. Theory Related Fields, pp.459-479, 1996.

R. Liptser and A. Shiryayev, Theory of martingales [42] R. Merton. Optimum consumption and portfolio rules in a continuoustime model, Journal of Economic Theory, vol.3, issue.4, pp.373-413, 1971.

H. Pham, Optimal stopping of controlled jump diffusion processes and viscosity solutions Comptes rendus de l'Académie des sciences, Mathématique, vol.1, issue.3209, pp.1113-1118, 1995.

M. Rásonyi, A remark on the superhedging theorem under transaction costs, Séminaire de Probabilités XXXVII, pp.394-398, 2003.
DOI : 10.1007/978-3-540-40004-2_17

A. Sayah, Equations d'Hamilton-Jacobi du premier ordre avec termes intégrodifferentiels: Parties I et II, 1991.

W. Schachermayer, The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time, Mathematical Finance, vol.26, issue.1, pp.19-48, 2004.
DOI : 10.1007/s001860050099

S. Shreve, Liquidity Premium for Capital Asset Pricing with Transaction Costs, Institute for Mathematics and Its Applications, vol.65, 1995.
DOI : 10.1007/978-1-4757-2435-6_9

S. Shreve and H. M. Soner, Optimal Investment and Consumption with Transaction Costs, The Annals of Applied Probability, vol.4, issue.3, pp.609-692, 1994.
DOI : 10.1214/aoap/1177004966

H. Soner, Optimal Control with State-Space Constraint I, SIAM Journal on Control and Optimization, vol.24, issue.3, p.552, 1986.
DOI : 10.1137/0324032

M. Soner, Optimal Control of Jump-Markov Processes and Viscosity Solutions, Institute for Mathematics and Its Applications, vol.10, p.501, 1988.
DOI : 10.1007/978-1-4613-8762-6_29