If (X t sim N left(0, sigma 2 t ight) ) and (Y t e X t ), calculate the pdf of (Y t ) Calculate ( mathbf E left Y t ight ) and (V left(Y t ight) ) Calculate the transition probability mathbf P left(Y t y mid Y t 0 y 0 ight) and give the density of this transition probability ...

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If (X_{t} sim Nleft(0, sigma^{2} t ight)) and (Y_{t}=e^{X_{t}}), calculate the pdf of (Y_{t}). Calculate (mathbf{E}left[Y_{t} ight])

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If $X_{t} \sim N\left(0, \sigma^{2} t\right)$ and $Y_{t}=e^{X_{t}}$, calculate the pdf of $Y_{t}$. Calculate $\mathbf{E}\left[Y_{t}\right]$ and $V\left(Y_{t}\right)$. Calculate the transition probability

\[\mathbf{P}\left(Y_{t}=y \mid Y_{t_{0}}=y_{0}\right)\]

and give the density of this transition probability.

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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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If (X_{t} sim Nleft(0, sigma^{2} t ight)) and (Y_{t}=e^{X_{t}}), calculate the pdf of (Y_{t}). Calculate (mathbf{E}left[Y_{t} ight])

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Quantitative Finance

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