Probability Theory
A type of time-symmetric forward–backward stochastic differential equations
[Un type d'équations différentielles stochastiques progressives–rétrogrades symétriques par rapport au temps]
Comptes Rendus. Mathématique, Tome 336 (2003) no. 9, pp. 773-778.

Nous étudions dans cette Note un type d'équations différentielles stochastiques progressives–rétrogrades symétriques par rapport au temps. Sous certaines conditions de monotonie, nous donnons un théorème d'existence et unicité des solutions des équations par une méthode de continuation. Ensuite nous présentons une application.

In this Note, we study a type of time-symmetric forward–backward stochastic differential equations. Under some monotonicity assumptions, we establish the existence and uniqueness theorem by means of a method of continuation. We also give an application.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00183-3
Peng, Shige 1 ; Shi, Yufeng 1

1 School of Mathematics and System Sciences, Shandong University, Jinan 250100, China
@article{CRMATH_2003__336_9_773_0,
     author = {Peng, Shige and Shi, Yufeng},
     title = {A type of time-symmetric forward{\textendash}backward stochastic differential equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {773--778},
     publisher = {Elsevier},
     volume = {336},
     number = {9},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00183-3},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00183-3/}
}
TY  - JOUR
AU  - Peng, Shige
AU  - Shi, Yufeng
TI  - A type of time-symmetric forward–backward stochastic differential equations
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 773
EP  - 778
VL  - 336
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S1631-073X(03)00183-3/
DO  - 10.1016/S1631-073X(03)00183-3
LA  - en
ID  - CRMATH_2003__336_9_773_0
ER  - 
%0 Journal Article
%A Peng, Shige
%A Shi, Yufeng
%T A type of time-symmetric forward–backward stochastic differential equations
%J Comptes Rendus. Mathématique
%D 2003
%P 773-778
%V 336
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(03)00183-3/
%R 10.1016/S1631-073X(03)00183-3
%G en
%F CRMATH_2003__336_9_773_0
Peng, Shige; Shi, Yufeng. A type of time-symmetric forward–backward stochastic differential equations. Comptes Rendus. Mathématique, Tome 336 (2003) no. 9, pp. 773-778. doi : 10.1016/S1631-073X(03)00183-3. http://www.numdam.org/articles/10.1016/S1631-073X(03)00183-3/

[1] Antonelli, F. Backward–forward stochastic differential equations, Ann. Appl. Probab., Volume 3 (1993), pp. 777-793

[2] Bensoussan, A. Stochastic Control by Functional Analysis Methods, North-Holland, Amsterdam, 1982

[3] Bismut, J.-M. Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl., Volume 44 (1973), pp. 384-404

[4] El Karoui, N.; Peng, S.; Quenez, M.-C. Backward stochastic differential equations in finance, Math. Finance, Volume 7 (1997), pp. 1-71

[5] Hu, Y.; Peng, S. Solution of forward–backward stochastic differential equations, Probab. Theory Related Fields, Volume 103 (1995), pp. 273-283

[6] Ma, J.; Protter, P.; Yong, J. Solving forward–backward stochastic differential equations explicitly – a four step scheme, Probab. Theory Related Fields, Volume 98 (1994), pp. 339-359

[7] Pardoux, E.; Peng, S. Adapted solution of a backward stochastic differential equation, Systems Control Lett., Volume 14 (1990), pp. 55-61

[8] Pardoux, E.; Peng, S. Backward doubly stochastic differential equations and systems of quasilinear parabolic SPDE's, Probab. Theory Related Fields, Volume 98 (1994), pp. 209-227

[9] Peng, S. Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics, Volume 37 (1991), pp. 61-74

[10] Peng, S. Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions, Stochastic Process. Appl., Volume 88 (2000), pp. 259-290

[11] Peng, S.; Shi, Y. Infinite horizon forward–backward stochastic differential equations, Stochastic Process. Appl., Volume 85 (2000), pp. 75-92

[12] Peng, S.; Wu, Z. Fully coupled forward–backward stochastic differential equations and applications to optimal control, SIAM J. Control Optim., Volume 37 (1999), pp. 825-843

[13] Yong, J. Finding adapted solutions of forward–backward stochastic differential equations – method of continuation, Probab. Theory Related Fields, Volume 107 (1997), pp. 537-572

Cité par Sources :