2. Let (2, F, P) be a probability space and let F = (Fn)nzo be a filtration. Given an F- predictable process (Hn)nz0, which is uniformly bounded, and an F-martingale (Xn)n>0, we define a process (Vn)n20 by n Vo = 0, V₁ = Hk(Xk – Xk-1). k=1 Prove that (V)nzo is still an F-martingale.

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2. Let (2, F, P) be a probability space and let F = (Fn)nzo be a filtration. Given an F-
predictable process (Hn)n20, which is uniformly bounded, and an F-martingale (Xn)n>0,
we define a process (vn)nzo by
n
Vo: 0, Vn:= - ΣΗ(Χ. - Χ.-1).
k=1
Prove that (V)nzo is still an F-martingale.
Transcribed Image Text:2. Let (2, F, P) be a probability space and let F = (Fn)nzo be a filtration. Given an F- predictable process (Hn)n20, which is uniformly bounded, and an F-martingale (Xn)n>0, we define a process (vn)nzo by n Vo: 0, Vn:= - ΣΗ(Χ. - Χ.-1). k=1 Prove that (V)nzo is still an F-martingale.
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