Let (X_{t}=W_{t}+u t) and (m_{t}^{X}=inf _{s leq t} X_{s}). Prove that, for (y <0, y

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Let $X_{t}=W_{t}+u t$ and $m_{t}^{X}=\inf _{s \leq t} X_{s}$. Prove that, for \(y<0, y

\[\mathbb{P}\left(m_{t}^{X} \leq y \mid X_{t}=x\right)=\exp \left(-\frac{2 y(y-x)}{t}\right)\]

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Mathematical Methods For Financial Markets

ISBN: 9781447125242

1st Edition

Authors: Monique Jeanblanc, Marc Yor, Marc Chesney

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Question Posted: Apr 02, 2024 06:00 AM

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Let (X_{t}=W_{t}+u t) and (m_{t}^{X}=inf _{s leq t} X_{s}). Prove that, for (y <0, y

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Mathematical Methods For Financial Markets

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