 Solution

A complete market is one in which every contingent claim in the pricing class can be replicated: for each finite maturity $T$ and terminal ${\mathcal{F}}_T$-measurable payoff $H$, there are an initial value and an admissible self-financing strategy whose terminal value is $H$ almost surely. It is enough for the complete market characterization to include all claims with bounded discounted payoffs. Thus every such payoff is attainable by trading the existing assets, rather than needing an additional independent security.