= Solution
{c}
For a long position in the claim, hold $-V_S$ shares and bank value $SV_S-V$ so that claim plus hedge has zero initial value. The <Black-Scholes equation> and <Itô's formula> show that the total position is <self-financing> and its Brownian and drift terms cancel. Equivalently, the positive replicating portfolio holds $V_S$ shares and bond value $V-SV_S$.
Under the usual growth, integrability and admissibility conditions, <no-arbitrage> forces the claim price to be $V$: a different price could be traded against the <replicating portfolio>. The qualification matters because an arbitrary formal PDE solution without a suitable financial class need not be a valid price.
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