Let (H) and (Z) be continuous semi-martingales. Check that the solution of the equation (X_{t}=H_{t}+int_{0}^{t} X_{s} d

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Let $H$ and $Z$ be continuous semi-martingales. Check that the solution of the equation $X_{t}=H_{t}+\int_{0}^{t} X_{s} d Z_{s}$, is

\[X_{t}=\mathcal{E}(Z)_{t}\left(H_{0}+\int_{0}^{t} \frac{1}{\mathcal{E}(Z)_{s}}\left(d H_{s}-d\langle H, Zangle_{s}\right)\right)\]

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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 (H) and (Z) be continuous semi-martingales. Check that the solution of the equation (X_{t}=H_{t}+int_{0}^{t} X_{s} d

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Mathematical Methods For Financial Markets

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