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We consider a one-dimensional Stochastic Differential Equation withreflection where we allow the drift to be merely bounded and measurable. It isalready known that such equations have a unique strong solution. Recently, ithas been shown that non-reflected SDE's with discontinuous drift possess moreregularity than one could expect, namely they are Malliavin differentiable andweakly differentiable w.r.t. the initial value. In this paper we show thatsimilar results hold for one-dimensional SDE's with reflection. We then applythe results to get a Bismut-Elworthy-Li formula for the correspondingKolmogorov equation.

A Note on the Malliavin Differentiability of One-Dimensional Reflected Stochastic Differential Equations with Discontinuous Drift