a) Compute the moment generating function mathbb E left exp left( beta int 0 T B t d B t ight)ight for all ( beta 1 T ) Expand ( left(B T ight) 2 ) using the It formula as in (4 30) b) Find the probability distribution of the stochastic integral ( beta int 0 T B t d B t ) ...

a Using 431 we have beginaligned mathbbEleftexp leftbeta int0T Bt d Btightight mathbbEleftmathrmebetaleftBT2Tight 2ight mathrmebeta T 2 mathbbEleftmathrmebetaleftBTight2 2ight fracmathrmebeta T 2sqrt2 ...

a) Compute the moment generating function [ mathbb{E}left[exp left(beta int_{0}^{T} B_{t} d B_{t}ight)ight] ] for all (beta

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a) Compute the moment generating function

\mathbb{E}\left[\exp \left(\beta \int_{0}^{T} B_{t} d B_{t}ight)ight]

for all $\beta<1 / T$.

Expand $\left(B_{T}ight)^{2}$ using the Itô formula as in (4.30).

b) Find the probability distribution of the stochastic integral $\beta \int_{0}^{T} B_{t} d B_{t}$.

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a) Compute the moment generating function [ mathbb{E}left[exp left(beta int_{0}^{T} B_{t} d B_{t}ight)ight] ] for all (beta

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a Using 431 we have beginaligned mathbbEleftexp leftbeta int0T Bt d Btightight mathbbEleftmathrmebetaleftBT2Tight 2ight mathrmebeta T 2 mathbbEleftmathrmebetaleftBTight2 2ight fracmathrmebeta T 2sqrt2 ...View the full answer

Introduction To Stochastic Finance With Market Examples

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