High-water mark tax boundary condition
= High-water mark tax boundary condition
{title2=$V_{\bar w}-\tau V_w=0$}
At an active maximum-raising boundary in <high-water mark investment taxation>, the finite-variation part of the <Itô formula> is $(V_{\bar w}-\tau V_w)d\bar w$, so smooth optimality sets this coefficient to zero. If the maximizing policy avoids increasing the maximum, the corresponding inequality $V_{\bar w}-\tau V_w\leq0$ is compatible with a <wealth-cap investment boundary> instead.