Let (Z ) be a complex BM (Z t X t i Y t ) Consider the two martingales ( left Z t ight 2 2 t ) and ( int 0 t left(X s d Y s Y s d X s ight) ) Prove that frac 1 2 left( left Z t ight 2 2 t ight) i int 0 t left(X s d Y s Y s d X s ight) ...

To prove the given expression is a martingale we can apply Its Lemma to leftZt ight2 which is a func ...

Let (Z) be a complex BM (Z_{t}=X_{t}+i Y_{t}). Consider the two martingales (left|Z_{t} ight|^{2}-2 t) and (int_{0}^{t}left(X_{s}

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Let $Z$ be a complex BM $Z_{t}=X_{t}+i Y_{t}$. Consider the two martingales $\left|Z_{t}\right|^{2}-2 t$ and $\int_{0}^{t}\left(X_{s} d Y_{s}-Y_{s} d X_{s}\right)$. Prove that

\[\frac{1}{2}\left(\left|Z_{t}\right|^{2}-2 t\right)+i \int_{0}^{t}\left(X_{s} d Y_{s}-Y_{s} d X_{s}\right)\]

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Mathematical Methods For Financial Markets

ISBN: 9781447125242

1st Edition

Authors: Monique Jeanblanc, Marc Yor, Marc Chesney

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Question Posted: Apr 02, 2024 06:00 AM

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Let (Z) be a complex BM (Z_{t}=X_{t}+i Y_{t}). Consider the two martingales (left|Z_{t} ight|^{2}-2 t) and (int_{0}^{t}left(X_{s}

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Mathematical Methods For Financial Markets

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