= Dividend-yield sensitivity of the perpetual put trigger
{title2=$\frac{dS^*}{d\delta}=\frac{X\beta_-}{\Delta(\beta_--1)^2}<0$}
Here $\Delta=\sqrt{(r-\delta-\sigma^2/2)^2+2r\sigma^2}$. Implicit differentiation of the negative-root equation gives $d\beta_-/d\delta=-\beta_-/\Delta>0$. Differentiating $S^*=X\beta_-/(\beta_--1)$ gives the displayed negative derivative. A higher proportional dividend yield lowers risk-neutral <stock> growth and makes waiting for lower <stock> prices more attractive to the put holder.
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