Finite branching bound in a complete market
= Finite branching bound in a complete market
{title2=$\#\operatorname{atoms}(\mathcal F_t)\leq n^t$}
With $n$ assets and a trivial initial sigma-field, <market completeness> forces at most $n$ positive-probability successors per current atom. Indicators of disjoint successor events are independent payoffs, whereas terminal holdings on a parent atom span at most $n$ asset-price functions. Iterating yields at most $n^t$ atoms at time $t$.