Abstract
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.
Citation
N. El Karoui. C. Kapoudjian. E. Pardoux. S. Peng. M. C. Quenez. "Reflected solutions of backward SDE's, and related obstacle problems for PDE's." Ann. Probab. 25 (2) 702 - 737, April 1997. https://doi.org/10.1214/aop/1024404416
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