We study reflected solutions of one-dimensional backward stochastic
differential equations. The “reflection” keeps the solution above
a given stochastic process. We prove uniqueness and existence both by a fixed
point argument and by approximation via penalization. We show that when the
coefficient has a special form, then the solution of our problem is the value
function of a mixed optimal stopping–optimal stochastic control problem.
We finally show that, when put in a Markovian framework, the solution of our
reflected BSDE provides a probabilistic formula for the unique viscosity
solution of an obstacle problem for a parabolic partial differential
equation.
Publié le : 1997-04-14
Classification:
Backward stochastic differential equation,
probabilistic representation of solution of second order
parabolic PDE,
obstacle problems for second order parabolic PDE,
60H10,
60H30,
35K85
@article{1024404416,
author = {El Karoui, N. and Kapoudjian, C. and Pardoux, E. and Peng, S. and Quenez, M. C.},
title = {Reflected solutions of backward SDE's, and related obstacle
problems for PDE's},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 702-737},
language = {en},
url = {http://dml.mathdoc.fr/item/1024404416}
}
El Karoui, N.; Kapoudjian, C.; Pardoux, E.; Peng, S.; Quenez, M. C. Reflected solutions of backward SDE's, and related obstacle
problems for PDE's. Ann. Probab., Tome 25 (1997) no. 4, pp. 702-737. http://gdmltest.u-ga.fr/item/1024404416/