Modern Stochastics: Theory and Applications

Bahlali, K., Hamadène, S., Mezerdi, B.: Backward stochastic differential equations with two reflecting barriers and continuous with quadratic growth coefficient. Stochastic Processes and their Applications 115, 1107–1129 (2005). MR2147243

Bender, C., Kohlmann, M.: BSDEs with Stochastic Lipschitz Condition. http://hdl.handle.net/10419/85163

Bismut, J.M.: Conjugate convex functions in optimal stochastic control. Journal of Mathematical Analysis and Applications 44(2), 384–40 (1973). MR0329726

Chung, K.: A Coure in Probability Theory. Academic Press (2001)

Crépey, S., Matoussi, A.: Reflected and doubly reflected bsdes with jumps: a priori estimates and comparison. Ann. Appl. Probab 18, 2041–2069 (2008)

Cvitanic, J., Karatzas, I.: Backward stochastic differential equations with reflection and dynkin games. The Annals of Probability 24(4), 2024–2056 (1996)

Dellacherie, C., Meyer, P.: Probabilités et Potentiel I-IV. Hermann, Paris (1975). MR0488194

El Karoui, N., Huang, S.J.: A general result of existence and uniqueness of backward stochastic differential equations. In: Pitman-Res-Notes-Math-Ser (ed.) Backward Stochastic Differential Equations. Springer, vol. 364, pp. 27–36 (1997)

El Karoui, N., Quenez, M.C.: Non-linear pricing theory and backward stochastic differential equations. Financial mathematics 1656, 191–246 (1997)

El Karoui, N., Peng, S., Quenez, M.C.: Backward stochastic differential equations in finance. Mathematical Finance 7(1), 1–71 (1997)

El Karoui, N., Kapoudjian, C., Pardoux, E., Peng, S., Quenez, M.C.: Reflected solutions of backward sde’s and related obstacle problems for pde’s. The Annals of Probability 25, 702–737 (1997). MR1434123

El Otmani, M.: Approximation scheme for solutions of bsdes with two reflecting barriers. Stochastic Analysis and Applications 26(1), 60–83 (2008)

El Otmani, M., Mrhardy, N.: Generalized bsde with two reflecting barriers. Random Operators and Stochastic Equations 16(4), 357–382 (2008)

Essaky, E., Ouknine, Y., Harraj, N.: Backward stochastic differential equation with two reflecting barriers and jumps. Stochastic Analysis and Applications 23, 921–938 (2005). MR2158885

Hamadène, S., Hassani, M.: Bsdes with two reflecting barriers : the general result. Probability Theory and Related Fields 132(2), 237–264 (2005)

Hamadène, S., Hdhiri, I.: Backward stochastic differential equations with two distinct reflecting barriers and quadratic growth generator. J. Appl. Math. Stoch. Anal 2006, 1–28 (2006)

Hamadène, S., Lepeltier, J.P.: Zero-sum stochastic differential games and backward equations. Systems and Control Letters 24(4), 259–263 (1995). MR1321134

Lepeltier, J.P., San Martin, J.: Backward sdes with two barriers and continuous coefficient: an existence result. Journal of applied probability 41(1), 162–175 (2004)

Li, M., Shi, Y.: Solving the double barriers reflected bsdes via penalization method. Statistics and Probability Letters 110, 74–83 (2016)

Pardoux, E.: Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic pdes of second order. Stochastic Analysis and Related Topics VI 42, 79–127 (1998)

Pardoux, E., Peng, S.: Adapted solution of a backward stochastic differential equation. Systems and Control Letters 1, 55–61 (1990)

Pardoux, E., Peng, S.: Backward stochastic differential equations and quasilinear parabolic partial differential equations. Stochastic partial differential Equations and their applications 176, 200–217 (1992)

Protter, P.: Stochastic Integration and Differential Equations. Springer, Berlin (1990)

Ren, Y., El Otmani, M.: Doubly reflected bsdes driven by a levy process. Nonlinear Analysis : Real World Applications 13, 1252–1267 (2012)

Saisho, Y.: Stochastic differential equations for multi-dimensional domain with reflecting boundary. Probab. Theory Related Fields 74, 455–477 (1987)

Wen, L.: Reflected BSDE with stochastic Lipschitz coefficient. https://arxiv.org/abs/0912.2162

Xu, M.: Reflected backward sdes with two barriers under monotonicity and general increasing conditions. Journal of Theoretical Probability 20(4), 1005–1039 (2007)

Yosida, K.: Functional Analysis. Springer, New York (1980)

Zheng, S., Zhou, S.: A generalized existence theorem of reflected bsdes with double obstacles. Statistics and Probability Letters 78(5), 528–536 (2007)