Compute the first and second moments of the time integral (int_{tau}^{T} S_{t} d t) for (tau in[0,
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Compute the first and second moments of the time integral \(\int_{\tau}^{T} S_{t} d t\) for \(\tau \in[0, T)\), where \(\left(S_{t}ight)_{t \in \mathbb{R}_{+}}\)is the geometric Brownian motion \(S_{t}:=S_{0} \mathrm{e}^{\sigma B_{t}+r t-\sigma^{2} t / 2}, t \geqslant 0\).
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We have beginalignedmathbbEleftinttauT St d tight inttauT mathbbEleftStight d t S0 inttauT mathbbEle...View the full answer
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Related Book For
Introduction To Stochastic Finance With Market Examples
ISBN: 9781032288277
2nd Edition
Authors: Nicolas Privault
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