 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2008/a/1/b/iii/solution

S \leq T

, then

{S \leq T} = Ω

. The previous result says that every

A \in F_{S}

equals

A \cap {S \leq T} \in F_{T}

. Thus

F_{S} \subseteq F_{T} .

Information known at the earlier stopping time remains known at the later stopping time.

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