Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 40 / 3 / a / Solution

A complete market permits claim replication for every finite maturity and every bounded claim measurable at that maturity: there are an initial capital and a predictable self-financing portfolio whose terminal wealth equals the claim almost surely. In a finite-state market this is equivalent to replicating every terminal payoff, since all such payoffs are bounded. Trading is allowed dynamically in the existing $n$ assets; adding a new security is not part of the definition.