B. Acciaio, Optimal risk sharing with non-monotone monetary functionals, Finance and Stochastics, vol.7, issue.2, pp.267-289, 2007.
DOI : 10.1007/s00780-007-0036-6

P. Artzner, F. Delbaen, J. M. Eber, and D. Heath, Coherent Measures of Risk, Mathematical Finance, vol.9, issue.3, pp.203-228, 1999.
DOI : 10.1111/1467-9965.00068

M. Avellaneda, A. Lévy, and A. Paras, 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

G. Barles, R. Buckdahn, and E. Pardoux, Backward stochastic differential equations and integral-partial differential equations, Stochastics and stochastic reports, pp.57-83, 1997.

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, Volume on Indifference Pricing, vol.30, issue.101 102, pp.71-113, 0118.

P. Barrieu and N. Karoui, Monotone stability of quadratic semimartingales with applications to general quadratic BSDEs and unbounded existence result, preprint, pp.19-81, 2011.

P. Barrieu, N. Cazanave, and N. Karoui, Closedness results for BMO semi-martingales and application to quadratic BSDEs, Comptes Rendus Mathematique, vol.346, issue.15-16, pp.881-886, 2008.
DOI : 10.1016/j.crma.2008.06.010
URL : https://hal.archives-ouvertes.fr/hal-00708491

D. Becherer, Bounded solutions to backward SDEs with jumps for utility optimization and indifference hedging, The Annals of Applied Probability, vol.16, issue.4, pp.2027-2054, 2006.
DOI : 10.1214/105051606000000475
URL : http://arxiv.org/abs/math/0702405

S. Biagini and M. Frittelli, On the extension of the Namioka-Klee theorem and on the Fatou property for risk measures. In Optimality and risk-modern trends in mathematical finance, pp.1-28, 2009.

K. Bichteler, Stochastic Integration and $L^p$-Theory of Semimartingales, The Annals of Probability, vol.9, issue.1, pp.49-89, 1981.
DOI : 10.1214/aop/1176994509

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

J. Bion-nadal, A new probabilistic approach to non local and fully non linear second order partial differential equations, preprint arXiv:1210, 1955.

J. Bion-nadal and M. Kervarec, Risk measuring under model uncertainty, The Annals of Applied Probability, vol.22, issue.1, 2011.
DOI : 10.1214/11-AAP766
URL : http://arxiv.org/abs/1004.5524

J. M. Bismut, Conjugate convex functions in optimal stochastic control, Journal of Mathematical Analysis and Applications, vol.44, issue.2, pp.384-404, 1973.
DOI : 10.1016/0022-247X(73)90066-8

K. Borch, Equilibrium in a reinsurance market, Econometrica, vol.30, 1962.

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

P. Briand and Y. Hu, BSDE with quadratic growth and unbounded terminal value, Probab. Theory Relat. Fields, pp.604-618, 2006.
DOI : 10.1007/s00440-006-0497-0
URL : http://arxiv.org/abs/math/0504002

P. Briand and Y. Hu, Quadratic BSDEs with convex generators and unbounded terminal conditions, Probability Theory and Related Fields, vol.14, issue.1, pp.543-567, 2008.
DOI : 10.1007/s00440-007-0093-y
URL : https://hal.archives-ouvertes.fr/hal-00136605

C. Burgert and L. Ruschendorf, On the optimal risk allocation problem, Statistics & Decisions, vol.24, issue.1/2006, pp.153-171, 2006.
DOI : 10.1524/stnd.2006.24.1.153

G. Carlier and R. Dana, Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints, Statistics & Decisions, vol.24, issue.1/2006, pp.127-152, 2006.
DOI : 10.1524/stnd.2006.24.1.127

G. Carlier and R. Dana, Are generalized call-spreads efficient?, Journal of Mathematical Economics, vol.43, issue.5, pp.581-596, 2007.
DOI : 10.1016/j.jmateco.2006.07.008
URL : https://hal.archives-ouvertes.fr/hal-00360142

G. Carlier, R. Dana, and N. Shahidi, Efficient insurance contracts under epsiloncontaminated utilities The Geneva Papers on Risk and Insurance Theory, pp.59-71, 2003.

A. Chateauneuf, R. Dana, and J. And-tallon, Optimal risk-sharing rules and equilibria with Choquet-expected-utility, Journal of Mathematical Economics, vol.34, issue.2, pp.191-214, 2000.
DOI : 10.1016/S0304-4068(00)00041-0
URL : https://hal.archives-ouvertes.fr/halshs-00451997

A. Chateauneuf and J. And-tallon, Diversification, convex preferences and non-empty core in the Choquet expected utility model, Economic Theory, vol.19, issue.3, pp.509-523, 2002.
DOI : 10.1007/s001990000152
URL : https://hal.archives-ouvertes.fr/halshs-00174770

A. Chateauneuf, F. Maccheroni, M. Marinacci, and J. And-tallon, Monotone continuous multiple priors, Economic Theory, vol.26, issue.4, pp.973-982, 2005.
DOI : 10.1007/s00199-004-0540-2
URL : https://hal.archives-ouvertes.fr/halshs-00177057

Z. Chen, A property of backward stochastic differential equations, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.326, issue.4, pp.483-488, 1998.
DOI : 10.1016/S0764-4442(97)89796-0

P. Cheridito, H. M. Soner, N. Touzi, and N. Victoir, Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs, Communications on Pure and Applied Mathematics, vol.1627, issue.7, pp.1081-1110, 2007.
DOI : 10.1002/cpa.20168
URL : http://arxiv.org/abs/math/0509295

G. Choquet, Theory of capacities, Annales de l???institut Fourier, vol.5, issue.30, pp.131-295, 1955.
DOI : 10.5802/aif.53

S. N. Cohen, Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces, Electronic Journal of Probability, vol.17, issue.0, p.62, 2011.
DOI : 10.1214/EJP.v17-2224

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

H. Cramér, On the mathematical theory of risk, Skandia Jubilee Volume, 1930.

S. Crépey and A. Matoussi, Reflected and doubly reflected BSDEs with jumps: A priori estimates and comparison, The Annals of Applied Probability, vol.18, issue.5, pp.2041-2069, 2008.
DOI : 10.1214/08-AAP517

J. Cvitani? and I. Karatzas, Convex Duality in Constrained Portfolio Optimization, The Annals of Applied Probability, vol.2, issue.4, pp.767-818, 1992.
DOI : 10.1214/aoap/1177005576

D. Finetti and B. , Su un'impostazione alternativa della teoria collettiva del rischio, Transactions XVth International Congress of Actuaries, 1957.

C. Dellacherie, M. , and P. , Probabilités et potentiel. Chapitre I à IV, 1975.

L. Denis, M. Hu, and S. Peng, Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths, Potential Analysis, vol.30, issue.8, pp.139-161, 2011.
DOI : 10.1007/s11118-010-9185-x

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

D. Denneberg, Non-additive measure and integral, Theory and Decision Library, Series B: Mathematical and Statistical Methods, pp.40-48, 1994.
DOI : 10.1007/978-94-017-2434-0

M. Denuit and A. Charpentier, Mathématiques de l'assurance non-vie. Tome 1 : principes fondamentaux de théorie du risque, Economica, 2004.

C. Doléans-dade and P. A. Meyer, Une caracterisation de BMO, Lecture Notes in Math, vol.581, issue.76, pp.383-389, 1977.
DOI : 10.1007/BFb0087206

J. Dow and S. R. Werlang, Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio, Econometrica, vol.60, issue.1, pp.197-204, 1992.
DOI : 10.2307/2951685

J. Eichberger and D. Kelsey, E-capacities and the Ellsberg paradox, Theory and Decision, vol.46, issue.2, pp.107-140, 1999.
DOI : 10.1023/A:1004994630014

E. Karoui and N. , Les Aspects Probabilistes Du Controle Stochastique, Lecture Notes in Mathematics, vol.876, pp.73-238, 1981.
DOI : 10.1007/BFb0097499

E. Karoui, N. Kapoudjian, C. Pardoux, E. Peng, S. Quenez et al., Reflected solutions of backward SDE's, and related obstacle problems for PDE's, The Annals of Probability, vol.25, issue.2, pp.702-737, 1997.
DOI : 10.1214/aop/1024404416

E. Karoui, N. Matoussi, A. Ngoupeyou, and A. , Quadratic BSDE with jumps and unbounded terminal condition, preprint, 2012.

E. Karoui, N. Nguyen, D. H. Jeanblanc-picqué, and M. , Compactification methods in the control of degenerate diffusions: existence of an optimal control, pp.169-219, 1987.

E. Karoui, N. Peng, S. Quenez, and M. C. , Backward Stochastic Differential Equations in Finance, Mathematical Finance, vol.7, issue.1, pp.1-71, 1994.
DOI : 10.1111/1467-9965.00022

E. Karoui, N. Ravanelli, and C. , CASH SUBADDITIVE RISK MEASURES AND INTEREST RATE AMBIGUITY, Mathematical Finance, vol.16, issue.4, pp.561-590, 2009.
DOI : 10.1111/j.1467-9965.2009.00380.x
URL : https://hal.archives-ouvertes.fr/hal-00708496

E. Karoui, N. Rouge, and R. , Pricing via utility maximization and entropy, Mathematical Finance, vol.10, issue.175, pp.259-276, 2000.

E. H. Essaky, Reflected backward stochastic differential equations with jumps and RCLL obstacle, preprint, 2006.

D. Filipovi? and G. Svindland, Optimal capital and risk allocations for law- and cash-invariant convex functions, Finance and Stochastics, vol.52, issue.3, pp.423-439, 2008.
DOI : 10.1007/s00780-008-0069-5

H. Föllmer and A. Schied, Stochastic Finance: An introduction in discrete time, second edition, de Gruyter studies in mathematics 27, pp.37-40, 2004.

M. Frittelli, R. Gianin, and E. , Putting order in risk measures, Journal of Banking & Finance, vol.26, issue.7, pp.1473-1486, 2002.
DOI : 10.1016/S0378-4266(02)00270-4

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

G. Greco, Integrale monotono, Rend. Sem. Mat. Padova, vol.57, pp.149-166, 1977.

S. Hamadène and Y. Ouknine, Reflected backward SDEs with general jumps, preprint, p.169, 2011.

Y. Hu, P. Imkeller, and M. Müller, Utility maximization in incomplete markets, The Annals of Applied Probability, vol.15, issue.3, pp.1691-1712, 2005.
DOI : 10.1214/105051605000000188

C. Hipp and M. Taksar, Optimal non-proportional reinsurance control, Insurance: Mathematics and Economics, vol.47, issue.2, pp.246-254, 2010.
DOI : 10.1016/j.insmatheco.2010.04.001

C. Hipp and M. Vogt, Optimal Dynamic XL Reinsurance, ASTIN Bulletin, vol.15, issue.02, pp.193-207, 2003.
DOI : 10.1016/S0167-6687(00)00049-4

M. Hu and S. Peng, G-Lèvy Processes under Sublinear Expectations, preprint, 2009.

W. Hürlimann, Excess of Loss Reinsurance with Reinstatements Revisited, ASTIN Bulletin, vol.XXIV, issue.01, pp.211-238, 2005.
DOI : 10.2143/AST.30.2.504640

M. Izumisawa, T. Sekiguchi, and Y. Shiota, Remark on a characterization of {BMO}-martingales, Tohoku Mathematical Journal, vol.31, issue.3, pp.281-284, 1979.
DOI : 10.2748/tmj/1178229795

J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, pp.129-132, 1987.
DOI : 10.1007/978-3-662-02514-7

J. Jacod, Calcul stochastique et problèmes de martingales, 1979.
DOI : 10.1007/BFb0064907

E. Jouini, W. Schachermayer, and N. Touzi, Law invariant risk measures have the Fatou propertyAdvances in mathematical economics, pp.49-71, 2006.

E. Jouini, W. Schachermayer, and N. Touzi, OPTIMAL RISK SHARING FOR LAW INVARIANT MONETARY UTILITY FUNCTIONS, Mathematical Finance, vol.3, issue.2, pp.269-292, 2008.
DOI : 10.1126/science.289.5485.1773
URL : https://hal.archives-ouvertes.fr/halshs-00176606

R. Karandikar, On pathwise stochastic integration, Stochastic Processes and their Applications, pp.11-18, 1995.
DOI : 10.1016/0304-4149(95)00002-O
URL : http://doi.org/10.1016/0304-4149(95)00002-o

N. Kazamaki, A sufficient condition for the uniform integrability of exponential martingales, Math. Rep. Toyama University, vol.2, pp.1-11, 1979.

N. Kazamaki, On transforming the class of {BMO}-martingales by a change of law, Tohoku Mathematical Journal, vol.31, issue.2, pp.117-125, 1979.
DOI : 10.2748/tmj/1178229832

N. Kazamaki, Continuous exponential martingales and BMO, pp.74-76, 1994.
DOI : 10.1007/BFb0073585

M. Kervarec, Etude des modèles non dominés en mathématiques financières, PhD Dissertation, 2008.

M. Kobylanski, Backward stochastic differential equations and partial differential equations with quadratic growth, Ann. Prob, vol.28, issue.116, pp.259-276, 2000.

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.

S. Kusuoka, On law invariant coherent risk measures Advances in mathematical economics, pp.83-95, 2001.

R. J. Laeven and M. A. Stadje, Robust portfolio choice and indifference valuation, preprint, 2012.
DOI : 10.1287/moor.2014.0646
URL : http://repository.tue.nl/733411

J. P. Lepeltier, S. Martin, and J. , Backward stochastic differential equations with continuous coefficient, Statistics & Probability Letters, vol.32, issue.4, pp.42-430, 1997.
DOI : 10.1016/S0167-7152(96)00103-4
URL : http://hdl.handle.net/10533/51192

D. Lépingle and J. Mémin, Sur l'int???grabilit??? uniforme des martingales exponentielles, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.22, issue.3, pp.175-203, 0194.
DOI : 10.1007/BF00641409

D. Lépingle and J. Mémin, Intégrabilité uniforme et dans L r des martingales exponentielles, Sém. Prob. de Rennes, pp.76-152, 0194.

X. Li and S. Tang, Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim, vol.32, issue.82, pp.1447-1475, 1994.

T. Lim and M. Quenez, Exponential Utility Maximization in an Incomplete Market with Defaults, Electronic Journal of Probability, vol.16, issue.0, pp.53-79, 2010.
DOI : 10.1214/EJP.v16-918
URL : https://hal.archives-ouvertes.fr/hal-00705764

Q. Q. Lin, Nonlinear Doob-Meyer Decomposition with Jumps, Acta Mathematica Sinica, English Series, vol.32, issue.1, pp.69-78, 2003.
DOI : 10.1007/s10114-002-0218-2

J. Ma and S. Yao, -Evaluations/Expectations and Related Analysis, Stochastic Analysis and Applications, vol.21, issue.4, pp.711-734, 2010.
DOI : 10.1214/aop/1019160253
URL : https://hal.archives-ouvertes.fr/hal-00018610

F. Maccheroni, M. Marinacci, A. Rustichini, and M. Taboga, PORTFOLIO SELECTION WITH MONOTONE MEAN-VARIANCE PREFERENCES, Mathematical Finance, vol.25, issue.3, pp.487-521
DOI : 10.1111/j.1467-9965.2009.00376.x

A. J. Mata, Abstract, ASTIN Bulletin, vol.17, issue.02, pp.349-368, 2000.
DOI : 10.2143/AST.26.1.563234

A. Matoussi, D. Possamai, and C. Zhou, Robust utility maximization in non-dominated models with 2BSDEs, Mathematical Finance, vol.159, pp.26-175, 2012.

R. Merton, Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case, The Review of Economics and Statistics, vol.51, issue.3, pp.239-265, 1969.
DOI : 10.2307/1926560

J. Mémin, Décompositions multiplicatives de semimartingales exponentielles et applications , Séminaire de probabilités de Strasbourg, pp.35-46, 1978.

P. Meyer, Une repr??sentation de surmartingales, pp.310-315, 1974.
DOI : 10.1007/BFb0057271
URL : http://archive.numdam.org/article/SPS_1974__8__310_0.pdf

M. A. Morlais, Equations différentielles stochastiques rétrogrades à croissance quadratique et applications, pp.70-79, 2007.

M. Morlais, Utility maximization in a jump market model, Stochastics and Stochastics Reports, pp.1-27, 2009.

J. Neveu, Discrete parameter martingale, 1975.

A. B. Ngoupeyou, Optimisation des portefeuilles d'actifs soumis au risque de défaut, p.70, 2010.

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

H. Panjer, Recursive Evaluation of a Family of Compound Distributions, ASTIN Bulletin, vol.XXXII, issue.01, pp.22-26, 1981.
DOI : 10.1057/jors.1966.8

E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems & Control Letters, vol.14, issue.1, pp.55-61, 1990.
DOI : 10.1016/0167-6911(90)90082-6

C. Partrat and J. Besson, Assurance non-vie. Modélisation, simulation, Economica, 2004.

S. Peng, Backward SDE and related g-expectation, in Backward stochastic differential equations, pp.141-159, 1997.

S. Peng, Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type, Prob. Theo. and Rel. Fields, pp.23-30, 1999.

S. Peng, G-Expectation, G-Brownian motion, and related stochastic calculus of Itô type, arXiv:math/0601035v2, p.55, 2007.

S. Peng, Nonlinear Expectations and Stochastic Calculus under Uncertainty, 2010.

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. Possamai and C. Zhou, Second order backward stochastic differential equations with quadratic growth, preprint, pp.172-183, 2010.

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

M. Royer, Backward stochastic differential equations with jumps and related nonlinear expectations, Stochastic Processes and their Applications, pp.1358-1376, 2006.

K. Sato, Lévy processes and infinitely divisible distributions, p.82, 1999.

D. Schmeidler, Integral representation without additivity, Proceedings of the American Mathematical Society, vol.97, issue.2, pp.255-261, 1986.
DOI : 10.1090/S0002-9939-1986-0835875-8

H. Schmidli, On minimizing the ruin probability by investment and reinsurance, The Annals of Applied Probability, vol.12, issue.3, pp.890-907, 2002.
DOI : 10.1214/aoap/1031863173

H. M. Soner, N. Touzi, and J. Zhang, Dual formulation of second order target problems, Ann. of App. Prob, to appear, pp.162-169, 2010.

H. M. Soner, N. Touzi, and J. Zhang, Quasi-sure Stochastic Analysis through Aggregation, Electronic Journal of Probability, vol.16, issue.0, pp.1844-1879, 2011.
DOI : 10.1214/EJP.v16-950
URL : http://arxiv.org/abs/1003.4431

H. M. Soner, N. Touzi, and J. Zhang, Wellposedness of second order BSDE's, Prob. Th. and Related Fields, pp.149-190, 0192.

D. W. Stroock and S. R. Varadhan, Multidimensional diffusion processes, p.24, 1979.
DOI : 10.1007/3-540-28999-2

B. Sundt, On excess of loss reinsurance with reinstatements. Bulletin of the Swiss Association of Actuaries, p.11, 1991.

M. Taksar, Optimal risk and dividend distribution control models for an insurance company, Mathematical Methods of Operations Research (ZOR), vol.51, issue.1, pp.1-42, 2000.
DOI : 10.1007/s001860050001

S. Tang and X. Li, Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps, SIAM Journal on Control and Optimization, vol.32, issue.5, pp.1447-1475, 1994.
DOI : 10.1137/S0363012992233858

R. Tevzadze, Solvability of backward stochastic differential equations with quadratic growth, Stochastic Processes and their Applications, vol.118, issue.3, pp.503-515, 2008.
DOI : 10.1016/j.spa.2007.05.009

M. Vogt, Optimale dynamische R??ckversicherung, Bl??tter der DGVFM, vol.2, issue.2, pp.407-420, 2004.
DOI : 10.1017/S051503610001343X

J. F. Walhin and J. Paris, Schadenexzedenten-R??ckversicherung mit Wiederauff??llung: Berechnung der Pr??mie und Ruinwahrscheinlichkeit des Zedenten, Bl??tter der DGVFM, vol.26, issue.1, pp.257-270, 2001.
DOI : 10.1007/BF02857112

S. Wang, Abstract, ASTIN Bulletin, vol.LXXXVII, issue.02, pp.213-234, 2002.
DOI : 10.2307/253675
URL : https://hal.archives-ouvertes.fr/hal-00953003

T. Zariphopoulou, Consumption-Investment Models with Constraints, SIAM Journal on Control and Optimization, vol.32, issue.1, pp.59-85, 1994.
DOI : 10.1137/S0363012991218827