The smallest g-supermartingale and reflected BSDE with single and double $L^2$ obstacles

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1. [1] M. Alario-Nazaret, J.P. Lepeltier, B. Marchal, Dynkin games, in: Lecture Notes in Control and Inform. Sci., vol. 43, Springer, Berlin, 1982, pp. 23-42. MR814103
2. [2] A. Bensoussan, A. Friedman, Non-linear variational inequalities and differential games with stopping times, J. Funct. Anal.16 (1974) 305-352. Zbl0297.90120MR354049
3. [3] J.M. Bismut, Sur un probleme de Dynkin, Z. Wahrsch. Verw. Gebiete39 (1977) 31-53. Zbl0336.60069MR444218
4. [4] J. Cvitanic, I. Karatzas, Backward stochastic differential equations with reflection and Dynkin games, Ann. Probab.24 (4) (1996) 2024-2056. Zbl0876.60031MR1415239
5. [5] F. Coquet, Y. Hu, J. Memin, S. Peng, Filtration-consistent nonlinear expectations and related g-expectations, Probab. Theory Related Fields123 (2002) 1-27. Zbl1007.60057MR1906435
6. [6] C. Dellacherie, P.A. Meyer, Probabilités et Potentiel, I–IV, Hermann, Paris, 1975. Zbl0323.60039MR488194
7. [7] C. Dellacherie, P.A. Meyer, Probabilités et Potentiel, V–VIII, Hermann, Paris, 1980. Zbl0464.60001MR488194
8. [8] E.B. Dynkin, A.A. Yushkevich, Theorems and Problems in Markov Processes, Plenum Press, New York, 1968. Zbl0181.44703
9. [9] N. El Karoui, Les aspects probabilistes du contrôle stochastique, in: Ecole d'été de Saint-Flour, 1979, Lecture Notes in Math., vol. 876, Springer, Berlin, 1981, pp. 73-238. Zbl0472.60002MR637471
10. [10] N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng, M.C. Quenez, Reflected solutions of backward SDE and related obstacle problems for PDEs, Ann. Probab.25 (2) (1997) 702-737. Zbl0899.60047MR1434123
11. [11] N. El Karoui, S.E. Peng, M.C. Quenez, Backward stochastic differential equations in finance, Math. Finance7 (1997) 1-71. Zbl0884.90035MR1434407
12. [12] S. Hamadène, Reflected BSDE's with discontinuous barrier and application, Stochastics Stochastics Rep.74 (3–4) (2002) 571-596. Zbl1015.60057MR1943580
13. [13] S. Hamadène, J.-P. Lepeltier, Reflected BSDE's and mixed game problem, Stochastics Process. Appl.85 (2000) 177-188. Zbl0999.91005MR1731020
14. [14] S. Hamadène, J.-P. Lepeltier, A. Matoussi, Double barrier backward SDEs with continuous coefficient, in: El Karoui N., Mazliak L. (Eds.), Pitman Res. Notes Math. Ser., vol. 364, 1997, pp. 161-171. Zbl0887.60065MR1752681
15. [15] I. Karatzas, S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer, New York, 1991. Zbl0734.60060MR1121940
16. [16] J.-P. Lepeltier, M. Xu, Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier, Preprint, 2004. Zbl1082.60059MR2185610
17. [17] H. Morimoto, Dynkin games and martingale methods, Stochastics13 (1984) 213-228. Zbl0569.60050MR762817
18. [18] J. Neveu, Discrete-Parameter Martingales, North-Holland, Amsterdam, 1975. Zbl0345.60026MR402915
19. [19] E. Pardoux, S. Peng, Adapted solutions of backward stochastic differential equations, Systems Control Lett.14 (1990) 51-61. Zbl0692.93064MR1037747
20. [20] S. Peng, Backward SDE and related g-expectation, in: El Karoui N., Mazliak L. (Eds.), Backward Stochastic Differential Equations, Pitman Res. Notes Math. Ser., vol. 364, 1997, pp. 141-159. Zbl0892.60066MR1752680
21. [21] S. Peng, Monotonic limit theory of BSDE and nonlinear decomposition theorem of Doob–Meyer's type, Probab. Theory Related Fields113 (1999) 473-499. Zbl0953.60059MR1717527
22. [22] S. Peng, Nonlinear expectations, nonlinear evaluations and risk measures, in: Lecture Notes in CIME–EMS, Bressanone, Italy, July, 2003, Lecture Notes in Math., Springer, 2004. Zbl1127.91032MR2113723
23. [23] S. Peng, Dynamical consistent nonlinear evaluations and expectations, Preprint, 2003. 
24. [24] A.V. Shorokhod, Studies in the Theory of the Random Processes, Addison-Wesley, New York, 1965. Zbl0146.37701MR185620

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