= Solution
\b[A complete market can replicate every contingent claim in its specified payoff class]: for every terminal $\mathcal F_T$-measurable payoff $X$, there is an admissible <self-financing portfolio> whose terminal wealth equals $X$ <almost surely>. Equivalently, in an arbitrage-free finite-state discrete-time model the <equivalent martingale measure> is unique. In notation,
$$
\boxed{\forall X\text{ in the claim class},\quad\exists\text{ self-financing }\theta\text{ with }V_T^\theta=X\text{ almost surely}.}
$$
<Market completeness> is a replication property. The following price comparisons also use the usual absence of <arbitrage>, which the source leaves implicit: without it the initial cost of <claim replication> need not be unique. For example, in a deterministic one-period model with cash worth one at both dates and a <stock> worth one initially but zero finally, all terminal claims are replicable using cash. Adding any <stock> holding changes the initial cost without changing the terminal payoff. This is a complete model with <arbitrage>, so it has no well-defined unique replication price.
Back to article page
