= High-water mark investment taxation
{title2=$dw=rw\,dt+\theta[\sigma\,dW+(\mu-r)\,dt]-c\,dt-\tau\,d\bar w$}
A high-water mark investment tax charges increments of historical maximum wealth $\bar w_t=\max(\bar w_0,\sup_{s\leq t}w_s)$ rather than every positive instantaneous return. For the convention charging $\tau\,d\bar w$, the <high-water mark tax boundary condition> is $V_{\bar w}=\tau V_w$ when the optimal policy raises the maximum. At sufficiently high tax, a <wealth-cap investment boundary> can make further maximum increases suboptimal.
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