Let (left(B_{t}ight)_{t in mathbb{R}_{+}})denote a standard Brownian motion. Given (T>0), find the stochastic integral decomposition of (left(B_{T}ight)^{3})

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Let $\left(B_{t}ight)_{t \in \mathbb{R}_{+}}$denote a standard Brownian motion. Given $T>0$, find the stochastic integral decomposition of $\left(B_{T}ight)^{3}$ as

\begin{equation*}

\left(B_{T}ight)^{3}=C+\int_{0}^{T} \zeta_{t, T} d B_{t} \tag{4.39}

\end{equation*}

where $C \in \mathbb{R}$ is a constant and $\left(\zeta_{t, T}ight)_{t \in[0, T]}$ is an adapted process to be determined.

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Introduction To Stochastic Finance With Market Examples

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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. Given (T>0), find the stochastic integral decomposition of (left(B_{T}ight)^{3})

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Taking expectation on both sides of 439 shows that beginaligned 0 mathbbEleft...View the full answer

Introduction To Stochastic Finance With Market Examples

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