One-period Gram-matrix replication formula
= One-period Gram-matrix replication formula
{title2=$H=Q^{-1}\mathbb E[P_1\xi_1],\quad Q=\mathbb E[P_1P_1^T]$}
In a one-period <complete market>, an invertible payoff <Gram matrix> identifies the unique holdings replicating each claim. The pricing weight is $Z=P_0^TQ^{-1}P_1$ and the random portfolio kernel is $W=Q^{-1}P_1$. Positive definiteness gives uniqueness of holdings; positivity of $Z$ requires an additional no-arbitrage condition.