Continuous dividend yield ($d{D}_t=\delta S_{t}dt$)

A proportional continuous dividend payment at rate $\delta$ per unit time relative to the ex-dividend stock price. The total gain of one share is $d{S}_t+\delta S_{t}dt$. Under a risk-neutral measure with short rate $r$, a geometric stock diffusion therefore has ex-dividend drift $(r-\delta )S_t$. A fixed cash dividend at a specified date is a different convention and generally requires an ex-dividend price jump.