Prove that if (X, Y) are two semi-martingales such that their stochastic logarithms are well defined, then

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Prove that if $X, Y$ are two semi-martingales such that their stochastic logarithms are well defined, then

\[\mathcal{L}(X Y)=\mathcal{L}(X)+\mathcal{L}(Y)+[\mathcal{L}(X), \mathcal{L}(Y)]\]

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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 03, 2024 01:01 AM

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Prove that if (X, Y) are two semi-martingales such that their stochastic logarithms are well defined, then

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To prove the given statement we first define the stochastic logarithm of a semimartingale Z as mathc...View the full answer

Mathematical Methods For Financial Markets

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