Week 8 Stopping times, martingales, strategies

This definition makes sense without extra mathematical technicalities if Xt is a continuous function of t and S is a closed set. In that case, Xτ ∈ S and Xt / ∈ S if t < τ . Many practical problems may be formulated using hitting times. When does something break? How long does it take to travel a given distance? A hitting time is an important example of the more general idea of a stopping time. A stopping time is a time that depends on the path X[0,T ], which makes it a random variable. What distinguishes a stopping time is that you know at time t whether τ ≤ t. If Ft is the filtration corresponding to Xt, then