Let (T>0) be fixed and let (varphi:[0, T] ightarrow mathbb{R}) be a bounded Borel function and

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Let $T>0$ be fixed and let $\varphi:[0, T] \rightarrow \mathbb{R}$ be a bounded Borel function and $N$ a Poisson process. Prove that there exist a predictable process $h$ and a constant $c$ such that

\[\exp \left(\int_{0}^{T} \varphi(s) d N_{s}\right)=c+\int_{0}^{T} h_{s} d N_{s}\]

Set $Z_{t}=\int_{0}^{t} \varphi(s) d N_{s}$. Then,

\[d e^{Z_{t}}=\left(e^{Z_{t^{-}}+\varphi(t)}-e^{Z_{t^{-}}}\right) d N_{t} .\]

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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 03, 2024 01:01 AM

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Let (T>0) be fixed and let (varphi:[0, T] ightarrow mathbb{R}) be a bounded Borel function and

Question:

Step by Step Answer:

To prove this statement well first show that the process Zt int0t varphis dNs satisfies the sto...View the full answer

Mathematical Methods For Financial Markets

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