Abstract
We deal with reflected backward stochastic differential equations (RBSDE) in a d-dimensional convex region with super-linear growth coefficient. We prove, in this setting, various existence and uniqueness results. This is done with an unbounded terminal data.
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Bahlali K.: Backward stochastic differential equations with locally Lipschitz coefficient, C. R. Acad. Sci. Paris Sér. I Math. 333 (2001) 481–486.
Bahlali K.: Existence and uniqueness of solutions for BSDEs with locally Lipschitz coefficient. Electron. Comm. Probab. 7 (2002) 169–179.
Bahlali K., Mezerdi B., Ouknine Y.: Some generic properties in backward stochastic differential equations with continuous coefficient, “Monte Carlo and probabilistic methods for partial differential equations (Monte Carlo, 2000)”.
Dermoune A., Hamadène S., Ouknine Y.: Backward stochastic differential equation with local time. Stochastics Stochastics Rep. 66 (1999) 103–119.
El Karoui N., Peng S., Quenez M.-C.: Backward stochastic differential equations in finance. Math. Finance 7 (1997) 1–71.
El Karoui N., Kapoudjian C., Pardoux É., Peng S., Quenez M.-C.: Reflected solutions of backward SDE’s and related obstacle problems for PDE’s, Ann. Probab. 25 (1997) 702–737.
Gégout-Petit A., Pardoux E.: Équations différentielles stochastiques rétrogrades réfléchies dans un convexe, Stochastics Stochastics Rep. 57 (1996) 111–128.
Hamadène S.: Multidimensional Backward SDE’s with uniformly continuous coefficients, Preprint Université du Maine 00–3, Le Mans 2000.
Hamadène S.: Équations différentielles stochastiques rétrogrades: le cas localement lipschitzien. Ann. Inst. H. Poincaré Probab. Statist. 32 (1996) 645–659.
Hamadène S., Lepeltier J.-P.: Zero-sum stochastic differential games and backward equations, Systems Control Lett. 24 (1995) 259–263.
Hamadène S., Ouknine Y.: Backward stochastic differential equations with jumps and random obstacle. To appear in Stochastics Stochastics Rep.
Lepeltier J.-P., San Martin J.: Backward stochastic differential equations with continuous coefficient, Statist. Probab. Lett. 32 (1997) 425–430.
Mao X.: Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients. Stochastic Process. Appl. 58 (1995) 281–292.
N’zi M.: Multivalued backward stochastic differential equations with local Lipschitz drift. Stochastics Stochastics Rep. 60 (1997) 205–218.
N’zi M., Ouknine Y.: Multivalued backward stochastic differential equations with continuous coefficients. Random Oper. Stochastic Equations 5 (1997) 59–68.
Ouknine Y.: Reflected backward stochastic differential equations with jumps, Stochastics Stochastics Rep. 65 (1998) 111–125.
Pardoux É., Peng S.: Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 (1990) 55–61.
Pardoux É., Râ¸scanu A.: Backward stochastic differential equations with subdifferential operator and related variational inequalities. Stochastic Process. Appl. 76 (1998) 191–215.
Rong S.: On solutions of backward stochastic differential equations with jumps and applications. Stochastic Process. Appl. 66 (1997) 209–236.
Saisho Y.: Stochastic differential equations for multidimensional domain with reflecting boundary. Probab. Theory Related Fields 74 (1987) 455–477.
Tang S.J., Li X.J.: Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim. 32 (1994) 1447–1475.
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© 2004 Springer Science+Business Media Dordrecht
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Bahlali, K., Essaky, E.H., Labed, B. (2004). Reflected Backward Stochastic Differential Equation with Super-Linear Growth. In: Albeverio, S., de Monvel, A.B., Ouerdiane, H. (eds) Proceedings of the International Conference on Stochastic Analysis and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2468-9_13
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DOI: https://doi.org/10.1007/978-1-4020-2468-9_13
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