= Deflator-based claim replication
{title2=$X_t=\mathbb E[Y_T\xi_T\mid\mathcal F_t]/Y_t$}
In a one-factor market whose filtration is the usual augmentation of the <natural Brownian filtration>, with nonzero <spot volatility> and <local martingale deflator> $Y$, the <Brownian martingale representation theorem> constructs a nonnegative <replicating strategy> for a bounded nonnegative <contingent claim>. The minimal initial cost among nonnegative <self-financing portfolios> is $\mathbb E[Y_T\xi_T]$.
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