 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2008/a/3/a/iii/solution

X_{n}

with

E ∣ X_{n} ∣ < \infty

for every

n

and

E (X_{n + 1} ∣ F_{n}) = X_{n} almost surely .

Adaptedness means that

X_{n}

F_{n}

-measurable. Iterating the tower property gives the analogous identity for any two deterministic times

m \leq n

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