• DOI:10.1214/AOP/1024404416
• Corpus ID: 53499425

Reflected solutions of backward SDE's, and related obstacle problems for PDE's

@article{Karoui1997ReflectedSO,
  title={Reflected solutions of backward SDE's, and related obstacle problems for PDE's},
  author={Nicole El Karoui and Christophe Kapoudjian and {\'E}tienne Pardoux and Shige Peng and Marie Claire Quenez},
  journal={Annals of Probability},
  year={1997},
  volume={25},
  pages={702-737}
}

• N. Karoui, C. Kapoudjian, +2 authors M. Quenez
• Published 1 April 1997
• Mathematics
• Annals of Probability

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.