M. Ben-artzi, P. Souplet, and F. B. Weissler, The local theory for viscous Hamilton???Jacobi equations in Lebesgue spaces, Journal de Math??matiques Pures et Appliqu??es, vol.81, issue.4, pp.343-378, 2002.
DOI : 10.1016/S0021-7824(01)01243-0

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

P. Briand and Y. Hu, BSDE with quadratic growth and unbounded terminal value, Probability Theory and Related Fields, vol.14, issue.4, pp.604-618, 2006.
DOI : 10.1007/s00440-006-0497-0

URL : https://hal.archives-ouvertes.fr/hal-00004619

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

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

M. G. Crandall, H. Ishii, and P. L. , user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

F. Delbaen, S. Peng, and E. R. Gianin, Representation of the penalty term of dynamic concave utilities, Finance and Stochastics, vol.39, issue.3, 2008.
DOI : 10.1007/s00780-009-0119-7

N. Karoui, S. Peng, and M. C. Quenez, Backward Stochastic Differential Equations in Finance, Mathematical Finance, vol.7, issue.1, pp.1-71, 1997.
DOI : 10.1111/1467-9965.00022

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

B. H. Gilding, M. Guedda, and R. Kersner, The Cauchy problem for ut=??u+|???u|q, Journal of Mathematical Analysis and Applications, vol.284, issue.2, pp.733-755, 2003.
DOI : 10.1016/S0022-247X(03)00395-0

URL : http://doi.org/10.1016/s0022-247x(03)00395-0

E. Jouini, W. Schachermayer, and N. Touzi, Law invariant risk measures have the Fatou property, Adv. Math. Econ, vol.9, issue.9, pp.49-71, 2006.
DOI : 10.1007/4-431-34342-3_4

URL : https://hal.archives-ouvertes.fr/halshs-00176522

M. Kobylanski, differential equations with quadratic growth, The Annals of Probability, vol.28, issue.2, pp.558-602, 2000.
DOI : 10.1214/aop/1019160253

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

E. Pardoux and S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations, Lecture Notes in Control and Inform. Sci, vol.176, pp.200-217, 1991.
DOI : 10.1007/BFb0007334