Past exam of the martingales and financial mathematics course of the University of Oxford / 2008 / A / 1 / a

A filtration is an increasing sequence of sub-sigma-algebras ${\mathcal{F}}_n\subseteq \mathcal{F}$: if $m\le n$, then ${\mathcal{F}}_m\subseteq {\mathcal{F}}_n$. It represents information available through each time.

A stopping time $T:\Omega \to {\mathbb{N}}_0\cup \{\infty \}$ satisfiesThus whether stopping has already occurred is determined by the current information.