J. Aubin and I. Ekeland, Applied Nonlinear Analysis, 1984.

T. Björk, Arbitrage theory,in continuous time, 1998.

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

H. Föllmer and A. Schield, Convex measures of risk and trading constraints, Finance and Stochastics, vol.6, issue.4, pp.429-447, 2002.
DOI : 10.1007/s007800200072

H. Föllmer and A. Schield, Stochastic finance : an introduction in discrete time, De Gruyter Studies in Math, 2002.

F. Hirsch and N. Bouleau, Dirichlet forms and analysis on Wiener space, De Gruyter Studies in Math, 1991.

I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, 1988.

M. Hu, L. Denis, and S. Peng, Function spaces and capacity related to a sublinear expectation : application to g-brownian motion pathes. Preprint, disponible sur http, 2008.

D. Lamberton and B. Lapeyre, Introduction au calcul stochastique appliqué à la finance. Ellipses, 1999.

A. Levy, M. Avellaneda, and A. Paras, Pricing and hedging derivative securities in markets with uncertain volatilities, Journal of Applied Finance, vol.1, 1995.

J. M. Eber, P. Artzner, F. Delbaen, and D. Heath, Thinking coherently, Risk, vol.10, pp.68-71, 1997.

J. M. Eber, P. Artzner, F. Delbaen, and D. Heath, Coherent measures of risk, Math. Finance, vol.9, issue.3, pp.203-228, 1999.

J. M. Eber, P. Artzner, F. Delbaen, and D. Heath, Coherent multiperiod risk adjusted values and bellman's principle, Annals of Operations Research, vol.152, issue.1, pp.5-22, 2007.

F. Delbaen, P. Cheredito, and M. Kupper, Dynamic monetary risk measures for bounded discrete time processes, Electronical Journal of Probability, vol.11, pp.57-106, 2006.

D. Revuz and M. Yor, Continuous Martingale and Brownian Motion, 1994.

W. Rudin, Functional Analysis, 1974.

W. Rudin, Analyse réelle et complexe, 1977.

C. Acerbi and D. Tasche, On the coherence of expected shortfall, Journal of Banking & Finance, vol.26, issue.7, pp.1487-1503, 2002.
DOI : 10.1016/S0378-4266(02)00283-2

C. Acerbi, C. Nordio, and . Sirtori, Expected shortfall as a tool for financial risk management. Working Paper, disponible sur http, 2001.

P. Barrieu and N. Karoui, Inf-convolution of risk measures and optimal risk transfer, Finance and Stochastics, vol.9, issue.2, pp.269-298, 2005.
DOI : 10.1007/s00780-005-0152-0

P. Barrieu and N. Karoui, Pricing, hedging and optimally designing derivatives via minimization of risk measures, 2007.

J. Bion, Conditional risk measure and robust representation of convex conditional risk measures, CMAP Preprint, vol.557, 2004.

J. Bion, Dynamic risk measures: Time consistency and risk measures from BMO martingales, Finance and Stochastics, vol.9, issue.2, pp.219-244, 2008.
DOI : 10.1007/s00780-007-0057-1

J. Bion, Time consistent dynamic risk processes, Stochastic Processes and their Applications, 2008.

F. Black and M. Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, vol.81, issue.3, pp.637-659, 1973.
DOI : 10.1086/260062

K. Borch, Equilibrium in a Reinsurance Market, Econometrica, vol.30, issue.3, pp.424-444, 1962.
DOI : 10.2307/1909887

A. S. Cherny, Pricing with coherent risk. Probability Theory and its applications, pp.506-540, 2007.

A. S. Cherny, Equilibrium with coherent risk. Preprint, available at, 2008.

G. Choquet, Theory of capacities Annales de l'Institut Fourier, pp.131-295, 1955.

G. Choquet, Forme abstraite du théorème de capacitabilité. Annales de l'Institut Fourier, pp.83-89, 1959.
DOI : 10.5802/aif.87
URL : http://archive.numdam.org/article/AIF_1959__9__83_0.pdf

M. Davis, Weather derivatives by marginal value, Quantitative Finance, vol.1, pp.1-4, 2001.
DOI : 10.1080/713665730
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.424.6682

F. Delbaen, A remark on slutsky's theorem. Séminaire de probabilités de Strasbourg, pp.313-315, 1999.

]. F. Delbaen, Coherent risk measures on general probability spaces Advances in finance and stochastics, pp.1-37, 2002.

F. Delbaen, The Structure of m???Stable Sets and in Particular of the Set of Risk Neutral Measures, Lecture Notes in Mathematics, vol.1874, pp.215-258, 2006.
DOI : 10.1007/978-3-540-35513-7_17

F. Delbaen and W. Schachermayer, A Compactness Principle for Bounded Sequences of Martingales with Applications, Proceedings of the Seminar of Stochastic Analysis, Random Fields and Applications, Progress in Probability, pp.137-173, 1999.
DOI : 10.1007/978-3-0348-8681-9_10

L. Denis and C. Martini, A theorical framework for the pricing of continent claims in the presence of model uncertainty. The Annals of Applied Probability, pp.827-852, 2006.

K. Detlefsen and G. Scandolo, Conditional and dynamic convex risk measures, Finance and Stochastics, vol.9, issue.4, 2005.
DOI : 10.1007/s00780-005-0159-6
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.453.4944

N. Karoui and M. Quenez, Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market, SIAM Journal on Control and Optimization, vol.33, issue.1, pp.29-66, 1995.
DOI : 10.1137/S0363012992232579

N. Karoui and N. Rouge, Pricing via utility maximisation and entropy, Mathematical Finance, vol.10, pp.259-276, 2000.

P. Embrechts, Extreme value theory : Potential and limitations as an integrated risk management tool, Derivatives Use, Trading and Regulations, vol.6, pp.449-456, 2000.

D. Feyel and A. De-la-pradelle, Espaces de Sobolev gaussiens, Annales de l???institut Fourier, vol.39, issue.4, pp.875-908, 1989.
DOI : 10.5802/aif.1193
URL : http://archive.numdam.org/article/AIF_1989__39_4_875_0.pdf

D. Filipovic and G. Svindland, Convex risk measures beyond bounded risks, or the canonical model space for law-invariant convex risk measures is l 1 . VIF working paper series, 2008.

M. Fritelli and E. R. Gianin, Dynamic convex risk measures. Risk Measures for the 21st Century, 2004.

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

P. Huber and V. Strassen, Minimax Tests and the Neyman-Pearson Lemma for Capacities, The Annals of Statistics, vol.1, issue.2, pp.251-263, 1973.
DOI : 10.1214/aos/1176342363

D. Kramkov and W. Schachermayer, The asymptotic elasticity of utility functions and optimal investement in incomplete markets, The Annals of Applied Probability, vol.9, issue.3, pp.904-950, 1999.

D. Kramkov and W. Schachermayer, Necessary and su ?cient conditions in the problem of optimal investment in incomplete markets, The Annals of Applied Probability, vol.13, issue.4, 2003.

F. 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

R. C. 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

S. Peng, Backward sde and related g-expectation

S. Peng, Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims, Acta Mathematicae Applicatae Sinica, English Series, vol.30, issue.2, pp.1-24, 2004.
DOI : 10.1007/s004400050214

S. Peng, Nonlinear expectations, nonlinear evaluations and risk measures Stochastics Methods in finance, pp.165-253, 2004.

S. Peng, NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS, Chinese Annals of Mathematics, vol.26, issue.02, pp.159-184, 2005.
DOI : 10.1142/S0252959905000154

S. Peng, G-expectation, g-brownian motion and related stochastic calculus of ito's type. Preprint, disponible sur http, 2006.

S. Peng, Multi-dimentional g-brownian motion and related stochastic calculus under g-expectation. Preprint, disponible sur http, 2006.
DOI : 10.1016/j.spa.2007.10.015
URL : http://doi.org/10.1016/j.spa.2007.10.015

S. Peng, Law of large numbers and central limit theorem under nonlinear expectations . Preprint, disponible sur http, 2007.

M. C. Quenez, Optimal Portfolio in a Multiple-Priors Model, Progress in Probability, pp.291-321, 2004.
DOI : 10.1007/978-3-0348-7943-9_18

F. Riedel, Dynamic coherent risk measures, Stochastic Processes and their Applications, pp.185-200, 2004.

H. Rootzén and C. Klüppelberg, A single number can't hedge against economic catastrophes, Ambio, vol.28, issue.6, pp.550-555, 1999.

A. Schied and C. Wu, Duality theory for optimal investments under model uncertainty, Statistics & Decisions, vol.23, issue.3/2005, pp.199-217, 2005.
DOI : 10.1524/stnd.2005.23.3.199

D. Talay and Z. Zheng, Worst case model risk management, Finance and Stochastics, vol.6, issue.4, pp.517-537, 2002.
DOI : 10.1007/s007800200074
URL : https://hal.archives-ouvertes.fr/inria-00072259

R. Tyrrell-rockafellar, Convex Analysis, 1970.
DOI : 10.1515/9781400873173

J. , V. Neumann, and O. Morgenstern, Theory of Games and Economic Behavior, 1944.