Smooth pasting
= Smooth pasting
{wiki}
= Smooth fit
{synonym}
At a regular exercise boundary for a diffusion <optimal stopping> problem, value matching is commonly accompanied by matching first derivatives. This makes the value $C^1$ across the boundary and eliminates a derivative-jump <local time of a semimartingale> term in the generalized <Itô formula>. It does not assert that second derivatives agree, or that smooth fit holds for every possible stopping problem.