= Black-Scholes equation with continuous stock dividends
{c}
{title2=$p_t+(\rho-\theta)xp_x+\frac12\sigma^2x^2p_{xx}-\rho p=0$}
When the underlying <stock> pays dividends at rate $\theta S_t$, its gain is $dS_t+\theta S_tdt$. Under the <risk-neutral measure> its ex-dividend drift is $(\rho-\theta)S_t$. A sufficiently smooth terminal-claim value obeys $p_t+(\rho-\theta)xp_x+\sigma^2x^2p_{xx}/2-\rho p=0$. These are dividends on the <stock>, not a source term paid by the claim itself.
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