Superhedging ($V_T\ge X$)

An admissible self-financing portfolio superhedges a contingent claim when its terminal wealth is at least the claim payoff almost surely. The least permitted initial cost is the superhedging price. Exact claim replication requires equality.

The infimum of initial costs of admissible superhedging portfolios. Positive pricing kernels supply lower bounds: if $\mathbb{E}[ZP]=p$ and $H\cdot P\ge X$, then $H\cdot p\ge \mathbb{E}[ZX]$ whenever these expectations exist.