# 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} }

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…

## 729 Citations

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