Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 8 (2003) > Paper 2 open journal systems 


Reflected Backward Stochastic Differential Equation with Jumps and Random Obstacle

Said Hamadène, Universite du Maine
Youssef Ouknine, Universite Cadi Ayyad


Abstract
In this paper we give a solution for the one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process. We prove existence and uniqueness of the solution in using penalization and the Snell envelope theory. However both methods use a contraction in order to establish the result in the general case. Finally, we highlight the connection of such reflected BSDEs with integro-differential mixed stochastic optimal control.


Full text: PDF

Pages: 1-20

Published on: February 3, 2003
Bibliography
  1. Barles, R. Buckdahn and E.Pardoux (1997). BSDEs and integral-partial differential equations, Stochastics 60, 57-83, Math. Review 98d:60110
  2. V.E.Benes (1970). Existence of optimal strategies based on specific information for a class of stochastic decision problems, SIAM JCO 8, 179-188, Math. Review 41 #9630
  3. C.Dellacherie (1972). Capacités et Processus Stochastiques, Springer Verlag , Math. Review 56 #6810
  4. C.Dellacherie and P.A.Meyer (1980). Probabilités et Potentiel, Hermann (Paris) Math. Review 82b:60001
  5. N.El-Karoui (1979). Les aspects probabilistes du contrôle stochastique, Ecole d'été de Saint-Flour, Lecture Notes in Mathematics 876, 73-238, Math. Review 83c:93062
  6. N.El-Karoui, C.Kapoudjian, E.Pardoux, S.Peng and M.C.Quenez (1997). Reflected solutions of backward SDE's and related obstacle problems for PDE's, Ann. Prob. 25 (2), 702-737, Math. Review 98k:60096
  7. S.Hamadène and J.P.Lepeltier (2000). Reflected Backward SDE's and Mixed Game Problems, Stoch. Proc. and their Appli. 85, 177-188, Math. Review 2001g:91025
  8. N. Ikeda and S. Watanabe (1981). Stochastic Differential Equations and Diffusion Processes, North Holland/Kodansha, Math. Review 90m:60069
  9. J.P. Lepeltier and B.Marchal (1977). Existence de politique optimale dans le contrôle intégro-différentiel, Annales de l'I.H.P. XIII (1), 45-97, Math. Review 56 #6894
  10. Y. Ouknine (1997). Multivalued backward stochastic differential Equations, Preprint, Université de Marrakech. MR number not available
  11. E.Pardoux, S.Peng (1990). Adapted Solutions of Backward Stochastic Differential Equations, Systems and Control Letters 14, 55-61, Math. Review 91e:60171
  12. R. Situ (1997). On solution of backward stochastic differential equations with jump and applications, Stoch. Proc. and their Appli. 66, 209-236. Math. Review 98j:60085
  13. S. Tang and X. Li (1994). Necessary condition for optimal control of stochastic systems with random jumps, SIAM JCO 32, 1447-1475, Math. Review 95j:49030
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489