M. Alario-nazaret, J. Lepeltier, and B. Marchal, Dynkin games, Stochastic Dierential Systems (Bad Honnef Workshop on stochastic processes), pp.23-32, 1982.
DOI : 10.1007/BFb0044285

P. Barrieu and N. Karoui, Optimal derivatives design under dynamic risk measures, Mathematics of Finance, Contemporary Mathematics (A.M.S. Proceedings), pp.13-26, 2004.
DOI : 10.1090/conm/351/06389
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.9667

E. Bayraktar, I. Karatzas, and S. Yao, Optimal Stopping for Dynamic Convex Risk Measures, Illinois Journal of Mathematics, vol.54, issue.3, pp.1025-1067, 2010.

J. 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 : http://doi.org/10.1016/0022-247x(73)90066-8

B. Bouchard, D. Possamaï, and X. Tan, A general Doob-Meyer-Mertens decomposition for g-supermartingale systems, Electronic Journal of Probability, vol.21, issue.36, 2016.
DOI : 10.1214/16-EJP4527
URL : https://hal.archives-ouvertes.fr/hal-01432984

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

C. Dellacherie and E. Lenglart, Sur des problemes de regularisation, de recollement et d'interpolation en theorie des processus, Sém. de Proba. XVI, lect. notes in Mathematics, vol.25, pp.298-313, 1981.
DOI : 10.5802/aif.577
URL : http://www.numdam.org/article/SPS_1982__16__298_0.pdf

R. Dumitrescu, M. Quenez, and A. Sulem, Generalized Dynkin Games and Doubly reected BSDEs with jumps, 2016.
DOI : 10.1214/16-ejp4568
URL : http://arxiv.org/abs/1310.2764

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

E. Karoui, N. Kapoudjian, C. Pardoux, E. Peng, S. et al., Reected solutions of Backward SDE's and related obstacle problems for PDE's, The Annals of Probability, pp.702-737, 1997.

E. Karoui, N. Peng, S. , 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

E. Karoui, N. , and M. Quenez, Non-linear Pricing Theory and Backward Stochastic Dierential Equations, Lect. Notes in Mathematics, vol.1656, 1997.

H. Essaky, Reflected backward stochastic differential equation with jumps and RCLL obstacle, Bulletin des Sciences Math??matiques, vol.132, issue.8, pp.690-710, 2008.
DOI : 10.1016/j.bulsci.2008.03.005
URL : http://doi.org/10.1016/j.bulsci.2008.03.005

L. I. Gal-'chouk, Optional martingales, Math. USSR Sbornik, vol.40, issue.4, pp.435-468, 1981.

M. Grigorova, P. Imkeller, Y. Ouknine, and M. Quenez, Doubly Reected BSDEs and Dynkin games: beyond the right-continuous case, 2016.

S. Hamadène, Reected BSDE's with discontinuous barrier and application, Stochastics and Stochastic Reports, vol.7434, pp.571-596, 2002.

S. Hamadène and Y. Ouknine, Backward stochastic dierential equations with jumps and random obstacle, Electronic Journal of Probability, vol.8, pp.1-20, 2003.

S. Hamadène and Y. Ouknine, Reflected backward SDEs with general jumps, Teoriya Veroyatnostei i ee Primeneniya, vol.60, issue.2, pp.357-376, 2015.
DOI : 10.4213/tvp4623

I. Karatzas and S. E. Shreve, Methods of mathematical nance, Applications of Mathematics, vol.39, 1998.

M. Kobylanski and M. Quenez, Optimal stopping time problem in a general framework, Electronic Journal of Probability, vol.17, issue.0, pp.1-28, 2012.
DOI : 10.1214/EJP.v17-2262
URL : https://hal.archives-ouvertes.fr/hal-01328196

M. Kobylanski and M. Quenez, Erratum: Optimal stopping time problem in a general framework, 2016.
DOI : 10.1214/ejp.v17-2262
URL : https://hal.archives-ouvertes.fr/hal-01328196

M. Kobylanski, M. Quenez, and M. Roger-de-campagnolle, Dynkin games in a general framework, Stochastics, vol.86, issue.2, pp.304-329, 2014.
DOI : 10.1080/17442508.2013.850203
URL : https://hal.archives-ouvertes.fr/hal-00795370

E. Lenglart, Tribus de Meyer et théorie des processus, Séminaire de probabilités de Strasbourg XIV, Lecture Notes in Mathematics, vol.79, issue.784, pp.500-546, 1978.
DOI : 10.1007/bfb0089512
URL : http://archive.numdam.org/article/SPS_1980__14__500_0.pdf

M. A. Maingueneau, Temps d???arret optimaux et theorie generale, Lecture Notes in Math, vol.77, issue.649, 1976.
DOI : 10.1007/BFb0064619

Y. Ouknine, Reected backward stochastic dierential equation with jumps, Stochastics and Stoch, Reports, vol.65, pp.111-125, 1998.
DOI : 10.1080/17442509808834175

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 Dierential equations and Quasilinear Parabolic Partial Dierential equations, Lect. Notes in CIS, vol.176, pp.200-217, 1992.
DOI : 10.1007/bfb0007334

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

S. Peng, Nonlinear Expectations, Nonlinear Evaluations and Risk Measures, Lecture Notes in Math, pp.165-253, 1856.
DOI : 10.1007/978-3-540-44644-6_4

M. Quenez and A. Sulem, BSDEs with jumps, optimization and applications to dynamic risk measures, Stochastic Processes and Their Applications, pp.0-29, 2013.
DOI : 10.1016/j.spa.2013.02.016
URL : https://hal.archives-ouvertes.fr/hal-00845018

M. Quenez and A. Sulem, Reected BSDEs and robust optimal stopping for dynamic risk measures with jumps, Stochastic Processes and their Applications, pp.3031-3054, 2014.
DOI : 10.1016/j.spa.2014.04.007
URL : http://arxiv.org/abs/1212.6744

E. Rosazza-gianin, Risk measures via -expectations, Insurance: Mathematics and Economics, vol.39, issue.1, pp.19-34, 2006.
DOI : 10.1016/j.insmatheco.2006.01.002

M. Royer, Backward stochastic dierential equations with jumps and related non-linear expectations, Stochastic Processes and Their Applications, pp.1358-1376, 2006.
DOI : 10.1016/j.spa.2006.02.009
URL : http://doi.org/10.1016/j.spa.2006.02.009

S. H. 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

. Gaborone and E. Botswana, -mail: oen@mopipi.ub.bw Département de, Mathématiques Faculté des Sciences Semlalia Université Cadi Ayyad B.P, p.2390