Let (left(B_{t}ight)_{t in mathbb{R}_{+}})denote a standard Brownian motion. a) Using the It isometry and the known relations

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Let $\left(B_{t}ight)_{t \in \mathbb{R}_{+}}$denote a standard Brownian motion.

a) Using the Itô isometry and the known relations

\[ B_{T}=\int_{0}^{T} d B_{t} \quad \text { and } \quad B_{T}^{2}=T+2 \int_{0}^{T} B_{t} d B_{t} \]

compute the third and fourth moments $\mathbb{E}\left[B_{T}^{3}ight]$ and $\mathbb{E}\left[B_{T}^{4}ight]$.

b) Give the third and fourth moments of the centered normal distribution with variance $\sigma^{2}$.

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Introduction To Stochastic Finance With Market Examples

ISBN: 9781032288277

2nd Edition

Authors: Nicolas Privault

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Question Posted: Feb 25, 2024 08:00 AM

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Let (left(B_{t}ight)_{t in mathbb{R}_{+}})denote a standard Brownian motion. a) Using the It isometry and the known relations

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a Using the It isometry 416 we have beginaligned mathbbEleftBT3ight mathbbEleftint0T d BtleftT2 int0...View the full answer

Introduction To Stochastic Finance With Market Examples

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