Show that the stochastic process [e^{int_{0}^{t} c(s) d B_{s}-frac{1}{2} int_{0}^{t} c^{2}(s) d s}] is a martingale for

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Show that the stochastic process

\[e^{\int_{0}^{t} c(s) d B_{s}-\frac{1}{2} \int_{0}^{t} c^{2}(s) d s}\]

is a martingale for any deterministic function $c(t)$. Does the result change if $c(t, \omega)$ is a stochastic process such that the stochastic integral is well defined?

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Quantitative Finance

ISBN: 9781118629956

1st Edition

Authors: Maria Cristina Mariani, Ionut Florescu

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Question Posted: Apr 20, 2024 05:57 AM

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Show that the stochastic process [e^{int_{0}^{t} c(s) d B_{s}-frac{1}{2} int_{0}^{t} c^{2}(s) d s}] is a martingale for

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To show that the stochastic process Xt eint0t cs d Bsfrac12 int0t c2s d s is a martingale we need to show that it satisfies the properties of a martin...View the full answer

Quantitative Finance

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