Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 39 / 3 / i

Table of contents
- Solution i

Solution

Relative to a filtration

(F_{t})

, a supermartingale is an adapted process

U_{t}

with

E ∣ U_{t} ∣ < \infty

for every

t

and

E [U_{t + 1} ∣ F_{t}] \leq U_{t} almost surely for every t .

By the tower property this also gives

E [U_{u} ∣ F_{t}] \leq U_{t}

for every

u \geq t

.

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