Infinite Horizon Reflected Backward SDEs with Jumps and RCLL Obstacle

REFERENCES

• Pardoux , E. , and Peng , S. 1990 . Adapted solutions of backward stochastic differential equations . Systems and Control Letters 14 : 51 – 61 .
   Google Scholar
• El Karoui , N. , and Mazliak , L. 1997 . Backward Stochastic Differential Equations . Number 364 in Pitman Research Notes in Mathematics . Addison, Wesley, Longman .
   Google Scholar
• Pardoux , E. , and Peng , S. 1992 . Backward stochastic differential equations and quasilinear parabolic partial differential equations . In Stochastic Differential Equations and Their Applications . Rozovskii , B. , Sowers , R. (Eds.), Lect. Not. Cont. Inf. Sci. , Vol. 176 , Springer , 200 – 217 .
   Google Scholar
• Barles , G. , and Lesigne , E. 1997 . SDE, BSDE, and PDE . In Backward Stochastic Differential Equations . El Karoui , N. , and Mazliak , L. (Eds.), Pitman Research Notes in Math. Series , 364 , Longman .
   Google Scholar
• Bally , V. , and Matoussi , A. Stochastic PDE's and doubly stochastic backward differentiable equations of theoretical probability .
   Google Scholar
• Tang , S. , and Li , X. 1994 . Necessary condition for optimal control of stochastic systems with random jumps . SIAM JCO 33 ( 2 ): 1447 – 1475 .
   Google Scholar
• Barles , G. , Buckdahn , R. , and Pardoux , E. 1997 . BSDEs and integral-partial differential equations . Stochastics 60 : 57 – 83 .
   Google Scholar
• El-Karoui , N. , Kapoudjian , C. , Pardoux , E. , Peng , S. , and Quenez , M.C. 1997 . Reflected solutions of backward SDE's and related obstacle problems for PDE's . Annals of Probability 25 : 702 – 737 .
   Web of Science ®Google Scholar
• Hamadène , S. , and Ouknine , Y. 2003 . Reflected backward stochastic differential equation with jumps and random obstacle . EJP 8 : 1 – 20 .
   Google Scholar
• Hamadène , S. 2006 . Mixed zero-sum differential game and American game options . To appear in SIAM JCO .
   Google Scholar
• Hamadène , S. , and Ouknine , Y. 2006 . Reflected backward stochastic differential equation with general jumps . Preprint, Université du Maine .
   Google Scholar
• Cvitanic , J. , and Karatzas , I. 1996 . Backward SDEs with reflection and Dynkin games . Annals of Probability 24 ( 4 ): 2024 – 2056 .
   Web of Science ®Google Scholar
• Peng , S. 1991. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stoch. Stoch. Rep. 37:61–74.
   Google Scholar
• Chen , Z. 1998 . Existence and uniqueness for BSDEs with stopping time . Chinese Science Bulletin 43 : 96 – 99 .
   Google Scholar
• Hamadène , L. , Lepeltier , J.P. , and Wu , Z. 1999 . Infinite horizon re- flected backward stochastic differential equations and applications in mixed control and game problems . Robability and Mathematical Statistics 19 : 211 – 234 .
   Google Scholar
• Dellacherie , C. , and Meyer , P.A. 1980 . Probabilités et Potentiel . Hermann , Paris .
   Google Scholar
• El-Karoui , N. Les aspects probabilistes du contrôle stochastique . In Ecole d’été de Saint-Flour . Lecture Notes in Mathematics. 876 , Springer Verlag , Berlin , 73 – 238 .
   Google Scholar
• Hamadène , S. 2002 . Reflected BSDE's with discontinuous barriers and application . Stochastics and Stochastics Reports 74 ( 3–4 ): 571 – 596 .
   Google Scholar
• Hamadène , S. , and Lepeltier , J.P. 2000 . Reflected backward SDE's and mixed game problems . Stochastic Processes and Their Applications 85 : 177 – 188 .
   Web of Science ®Google Scholar
• Ikeda , N. , and Watanabe , S. 1981 . Stochastic Differential Equations and Diffusion Processes . North Holland/Kodansha .
   Google Scholar
• Lepeltier , J.P. , and Mingyu , X. 2005 . Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier . Statist. Probab. Lett. 75 ( 1 ): 58 – 66 .
   Web of Science ®Google Scholar
• Mingyu , X. , and Peng , S. 2005 . The smallest g-supermartingale and reflected BSDE with single and double L2 obstacles . Annales de l'IHP (B), Probability and Statistics . 41 ( 3 ): 605 – 630 .
   Google Scholar
• Pardoux , E. 1999 . BSDEs, weak convergence, and homogenization of semilinear PDEs . In Nonlin. Anal. Dif. Equa. and Control . Clarke , F. , and Stern , R. (Eds.), Kluwer Acad. Publi. , Netherlands , 503 – 549 .
   Google Scholar
• Situ , R. 1997 . On solution of backward stochastic differential equations with jump and applications . Stochastic Processes and Their Applications 66 : 209 – 236 .
   Web of Science ®Google Scholar