S. Ankirchner, C. Blanchet-scalliet, and A. Elyraud-loisel, CREDIT RISK PREMIA AND QUADRATIC BSDEs WITH A SINGLE JUMP, International Journal of Theoretical and Applied Finance, vol.1579, issue.07, pp.1103-1129, 2010.
DOI : 10.1007/BFb0089484

URL : https://hal.archives-ouvertes.fr/hal-00402313

G. Barles, R. Buckdahn, and E. Pardoux, Backward stochastic differential equations and integral-partial differential equations, Stochastics and Stochastic Reports, vol.10, issue.6, pp.57-83, 1997.
DOI : 10.1137/S0363012992233858

M. T. Barlow and P. Protter, On convergence of semimartingales, pp.188-193, 1990.
DOI : 10.1007/BFb0064636

P. Barrieu, E. Karoui, and N. , Monotone stability of quadratic semimartingales with applications to general quadratic BSDE's and unbounded existence. The Annals of Probability, pp.1831-1863, 2013.

P. Barrieu, N. Karoui, and . Pricing, Hedging and Optimally Designing Derivatives via Minimization of Risk Measures, the book " Indifference Pricing: Theory and Applications, 2008.

D. Becherer, Utility-indifference hedging and valuation via reaction-diffusion systems, Proc .Roy. Soc, pp.460-487, 2004.
DOI : 10.1098/rspa.2003.1234

URL : http://www.math.tu-berlin.de/~becherer/utilityindifference.pdf

D. Becherer, Bounded solutions to Backward SDE's with jump for utility optimization and indifference hedging, The Annals of Applied Probability, pp.2027-2054, 2006.

D. Becherer, M. Butner, and K. Kentia, On the monotone stability approach to BSDE with jumps Extensions, concrete criteria and examples, 2016.

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

URL : https://doi.org/10.1016/0022-247x(73)90066-8

G. Bordigoni, A. Matoussi, and M. Schweizer, A Stochastic Control Approach to a Robust Utility Maximization Problem, Stochastic Analysis and Applications . Proceedings of the Second Abel Symposium, pp.125-151, 2005.
DOI : 10.1007/978-3-540-70847-6_6

L. Boccardo, F. Murat, and J. P. Puel, Existence de solutions faibles pour deséquationsélliptiquesdeséquations deséquationsélliptiques quasi-linéaireslinéairesà croissance quadratique, Nonlinear Partial Differential Equations and Their Applications Research Notes in Math, pp.19-73, 1983.

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 : 10.1016/S0764-4442(97)80108-5

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

P. Briand and Y. Hu, BDSE convex confficient and unbounded terminal value
DOI : 10.1007/s00440-007-0093-y

C. Dellacherie, Capacités et processus stochastiques, 1972.

C. Dellacherie, Inégalités de convexité pour les processus croissants et les sousmartingales Séminaire de Probabilités (Strasbourg) XIII, pp.371-377, 1977.
DOI : 10.1007/bfb0070876

F. Delbaen and S. Tang, Harmonic analysis of stochastic equations and backward stochastic differential equations, Probability theory and Related Fields, pp.291-336, 2010.

D. Duffie and L. G. Epstein, Stochastic Differential Utility, Econometrica, vol.60, issue.2, pp.353-394, 1992.
DOI : 10.2307/2951600

URL : http://www.darrellduffie.com/uploads/pubs/DuffieEpstein1992.pdf

E. Karoui and N. , Les Aspects Probabilistes Du Controle Stochastique, Lecture Notes in Mathematics, vol.876, pp.73-238, 1982.
DOI : 10.1007/BFb0097499

E. Karoui, N. Mazliak, and L. , Backward Stochastic Diffential Equations, Pitman Res. Notes Math. Ser. Longman Harlow, vol.364, 1997.

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

E. Karoui, N. Rouge, and R. , Pricing via Utility Maximization and Entropy, Mathematical Finance, vol.10, pp.259-276, 2000.

E. Karoui, N. Hamadène, and S. , BSDEs and risk-sensitive control, zero-sum and nonzerosum game problems of stochastic functional differential equations, Stochastic Processes and their Applications, pp.145-169, 2003.

E. Karoui, N. Hamadène, S. Matoussi, and A. , Backward stochastic differential equations and applications. Chapter 8 in the book " Indifference Pricing: Theory and Applications, Princeton Series in Financial Engineering, pp.267-320, 2008.

W. H. Fleming and S. J. Sheu, Risk-Sensitive Control and an Optimal Investment Model, Mathematical Finance, vol.10, issue.2, pp.197-213, 2000.
DOI : 10.1111/1467-9965.00089

URL : http://www.math.sinica.edu.tw/www/file_upload/sheusj/paper11.pdf

W. H. Fleming and S. J. Sheu, Risk-sensitive control and an optimal investment model II, The Annals of Applied Probability, vol.12, issue.2, pp.730-767, 2002.
DOI : 10.1214/aoap/1026915623

URL : https://doi.org/10.1214/aoap/1026915623

S. Hamadène, Equation différentielles stochastiques rétrogrades : le cas localement lipschitzien, Ann. Inst. Henri Poincaré, vol.32, issue.5, pp.645-659, 1996.

S. Hamadène and Y. Ouknine, BSDE with local time, Stochastic and Stochastic Reports, pp.103-119, 1999.

M. Jeanblanc and L. Cam, Immersion Property and Credit Risk Modelling
DOI : 10.1007/978-3-642-02608-9_6

URL : http://www.maths.univ-evry.fr/prepubli/262.pdf

M. Jeanblanc, A. Matoussi, and A. Ngoupeyou, Robust utility maximization problem in a discontinuous filtration, 2013.

M. Jeanblanc, A. Matoussi, and A. Ngoupeyou, Indifference Pricing of Unbounded Credit Derivatives, 2012.

Y. Jiao and H. Pham, Optimal investment with counterparty risk: a??default-density model approach, Finance and Stochastics, vol.2, issue.4, pp.725-753, 2011.
DOI : 10.1007/BFb0088224

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

URL : http://arxiv.org/pdf/math/0508448

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

URL : http://doi.org/10.1214/aop/1019160253

S. Kusuoka, A Remark on default risk models, Adv. Math. Econ, vol.1, pp.69-82, 1999.
DOI : 10.1007/978-4-431-65895-5_5

A. Lazrak and M. Quenez, A Generalized Stochastic Differential Utility, Mathematics of Operations Research, vol.28, issue.1, pp.154-180, 2003.
DOI : 10.1287/moor.28.1.154.14259

URL : https://hal.archives-ouvertes.fr/hal-00485718

J. Lepeltier and J. San-martin, Backward stochastic differential equations with continuous coefficient, Statistics & Probability Letters, vol.32, issue.4, pp.425-430, 1997.
DOI : 10.1016/S0167-7152(96)00103-4

D. Lepingle 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, 1978.
DOI : 10.5802/aif.557

T. Lim and M. Quenez, Exponential Utility Maximization in an Incomplete Market with Defaults, Electronic Journal of Probability, vol.16, issue.0, pp.1434-1464, 2011.
DOI : 10.1214/EJP.v16-918

URL : https://hal.archives-ouvertes.fr/hal-00705764

J. Ma and J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications, Lecture Notes in Mathematics, vol.1702, 1999.
DOI : 10.1007/978-3-540-48831-6

M. Mania and M. Schweizer, Dynamic exponential utility indifference valuation. The Annals of Applied Probability, pp.2113-2143, 2005.
DOI : 10.1214/105051605000000395

URL : http://doi.org/10.1214/105051605000000395

M. Mania and R. Tevzadze, An exponential Martingale Equation, Elect. Comm. in Probab, vol.11, pp.206-216, 2006.

P. A. Meyer and C. Yoeurp, Sur la décomposition multiplicative des sous-martingales positives, pp.501-504, 1976.

A. Morlais, utility maximization in a jump market model, Stochastics, pp.1-27, 2009.

E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems and Control Letters, pp.55-61, 1990.

S. Peng, Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type. Proba. Theory Rel, pp.473-499, 1999.

S. Peng, Nonlinear Expectations and Risk Measures, Proceedings of the CIME-EMS summer school, pp.6-12, 2003.
DOI : 10.1007/978-3-540-44644-6_4

S. Peng, Nonlinear Expectations, Nonlinear Evaluations and Risk mesaures, pp.165-253, 2004.
DOI : 10.1007/978-3-540-44644-6_4

S. Peng and M. Y. Xu, G ? -expectation and the related non-linear Doob-Meyer decomposition theorem. Control Theory and Related Topics, pp.122-140, 2007.

M. Yor, Sur les inégalités optionnelles et une suite remarquable de formule exponentielle, 1975.
DOI : 10.1007/bfb0101123