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Abstrakty
We prove existence and uniqueness results of the solution for infinite horizon reflected backward stochastic differential equations with one or two barriers. We also apply these results to get the existence of optimal control strategy for the mixed control problem and a saddle-point strategy for the mixed game problem when, in both situations, the horizon is infinite.
Czasopismo
Rocznik
Tom
Strony
211--234
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Laboratoire Statistique et Processus, Université du Maine, 72085 Le Mans Cedex 9, France
autor
- Laboratoire Statistique et Processus, Université du Maine, 72085 Le Mans Cedex 9, France
autor
- School of Mathematics and System Sciences, Shandong University, Jinan 250100, P.R. China
Bibliografia
- [1] M. Alario-Nazaret, Jeux de Dynkin, Thèse de Doctorat en mathématiques, Université de Franche-Comté, France, 1982.
- [2] V. E. Benes, Existence of optimal strategies based on specified information for a class of stochastic decision problems, SIAM J. Control Optim. 8 (1970), pp. 179-188.
- [3] A. Bensoussanet J.-L. Lions, Applications des inéquations variationnelles en contrôle stochastique, Dunod, Paris 1979.
- [4] Z.Chen, Existence and uniqueness for BSDE's with stopping time, Chinese Science Bulletin 43 (1998), pp. 96-99.
- [5] J. Cvitanic and I. Karatzas, Backward SDE’S with reflection and Dynkin games, Ann. Probab. 24 (4) (1996), pp. 2024-2056.
- [6] M. H. A. Davis and R. Elliott, Optimal play in a stochastic differential game, SIAM J. Control. Optim. 19 (4) (1981).
- [7] C. Dellacherie, Capacités et processus stochastiques, Springer, Berlin 1972.
- [8] - et P.-A. Meyer, Probabilités et potentiel, Chap. V-VIII, Hermann, Paris 1980.
- [9] D. Duffie and L. Epstein, Stochastic differential utility, Econometrica 60 (1992), pp. 353-394.
- [10] R. Elliott, The existence of value in stochastic differential games, SIAM J. Control Optim. 14 (1) (1976).
- [11] N. El-Karoui, Les aspects probabilistes du contrôle stochastique, in: Ecole d’Eté de Saint-Flour, Lecture Notes in Math. 876, Springer, Berlin 1979, pp. 73-238.
- [12] - C. Kapoudjian, E. Pardoux, S. Peng and M.-C. Quenez, Reflected solutions of backward SDE's and related obstacle problems for PDE's, Ann. Probab. 25 (2) (1997), pp. 702-737.
- [13] N. El-Karoui, S. Peng and M.-C. Quenez, Backward stochastic differential equation in finance, Math Finance 7 (1997), pp. 1-71.
- [14] S. Hamadène and J.-P. Lepeltier, Zero-sum stochastic differential games and backward equations, Systems Control Lett. 24 (1995), pp. 259-263.
- [15] - Backward equations, stochastic control and zero-sum stochastic differential games, Stochastics and Stochastic Reports 54 (1995), pp. 221-231.
- [16] - Reflected backward SDE's, mixed control and game problems, Preprint 1999.
- [17] I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, 2nd edition, Springer, New York 1991.
- [18] E. Pardoux and S. Peng, Adapted solutions of a backward stochastic differential equation, Systems Control Lett. 14 (1990), pp. 55-61.
- [19] - Backward stochastic differential equations and quasilinear parabolic partial differential equations, Lecture Notes in Control and Inform. Sci. 176, Springer, 1992, pp. 200-217.
- [20] S. Peng, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics 37 (1991), pp. 61-74.
- [21] D. Revuz, Continuous Martingales and Brownian Motion, Springer, New York 1994.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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