= Solution
Take the original measure as the <risk-neutral measure> for this zero-interest model, or interpret $S$ as a discounted <stock> price. \b[$\xi_t$ is the arbitrage-free value of the European contingent claim with payoff $g(S_T)$], and \b[$\pi_t$ is its option delta and replicating stock holding]. Part (b) supplies the <self-financing portfolio>:
$$
\boxed{\text{stock holding }\pi_t=V_S(t,S_t),\qquad
\text{cash holding }\xi_t-\pi_tS_t.}
$$
With the cash asset identically one, its value is $\xi_t$ and its gains satisfy $d\xi_t=\pi_t\,dS_t$, so it exactly replicates $g(S_T)$. This <delta hedge> is admissible since the assumed nonnegative $V$ gives nonnegative wealth. In this continuous-path setting the holdings can be taken <predictable>.
The auxiliary <change of measure> in part (c) expresses the <option delta> as an <expectation> of terminal payoff sensitivity. It changes the <stock> drift to $aa'$ and is generally not the original <risk-neutral measure> for the zero-interest stock market. Its role is to value sensitivity under the tilted state dynamics, while the actual <replicating strategy> trades under the original dynamics. No general claim of <market completeness> is needed, including when $a$ can vanish.
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