Exercise 6.12 (Doobs Decomposition) For an integrable process {X(t)} adapted to the filtration {Ft}, define with D(0)

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Exercise 6.12 (Doob’s Decomposition) For an integrable process {X(t)}

adapted to the filtration {Ft}, define

with D(0) = 0. Show that the process {M(t)} defined by M(t) = Σt k=0 D(k)
is a martingale and the process {A(t)} defined by A(t) = X(t) − M(t) is predictable.

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Stochastic Processes With Applications To Finance

ISBN: 9781439884829

2nd Edition

Authors: Masaaki Kijima

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Question Posted: Sep 19, 2024 07:03 PM

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Exercise 6.12 (Doobs Decomposition) For an integrable process {X(t)} adapted to the filtration {Ft}, define with D(0) = 0. Show that the process {M(t)} defined by M(t) = t k=0 D(k) is a martingale...
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Exercise 6.12 (Doobs Decomposition) For an integrable process {X(t)} adapted to the filtration {Ft}, define with D(0)

Question:

D(t) = X(t)-Et-1[X(t)], t = 1,2,..., T,

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Stochastic Processes With Applications To Finance

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