= Solution
{c}
Under the pricing measure, the ex-dividend stock drift is $r-\delta=0.04$. Thus
$$
\boxed{V(t,S_t)=2e^{-0.05(T-t)}\mathbb E^Q[S_T\mid\mathcal F_t]
=2S_t e^{-0.01(T-t)}.}
$$
A direct replication holds $2e^{-\delta(T-t)}$ shares and reinvests every dividend into more shares. The share count grows at rate $\delta$, reaching two shares at expiry, with no external cash input. This payoff contains only the terminal ex-dividend stock value, unlike part (b), which also includes the separately accumulated dividends.
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