  In this article, we build upon the work of Soner, Touzi and Zhang [Probab.
Theory Related Fields 153 (2012) 149-190] to define a notion of a second order
backward stochastic differential equation reflected on a lower c\`adl\`ag
obstacle. We prove existence and uniqueness of the solution under a
Lipschitz-type assumption on the generator, and we investigate some links
between our reflected 2BSDEs and nonclassical optimal stopping problems.
Finally, we show that reflected 2BSDEs provide a super-hedging price for
American options in a market with volatility uncertainty.
