Solution
= Solution
For the linear spatial factor, $f''=0$ and $Sf'=f$. Hence $\lambda=r-q$ and $g'=qg$. Absorbing the constant $k$ into the time-factor amplitude gives \b[$\boxed{V(S,t)=A S e^{q(t-T)}}$]. In particular a terminal claim equal to $AS_T$ is worth $AS e^{-q(T-t)}$, as expected for an asset paying a continuous dividend yield.