We consider a contingent claim with a terminal payoff (h left(S T ight) ) and a continuous payoff ( left(x s , s leq T ight) ), where (x s ) is paid at time (s ) Prove that the price of this claim is V t mathbb E mathbb Q left(e r(T t) h left(S T ight) int t T e r(s t) x s d s mid mathcal F t ight)...

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We consider a contingent claim with a terminal payoff (hleft(S_{T} ight)) and a continuous payoff (left(x_{s}, s

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We consider a contingent claim with a terminal payoff $h\left(S_{T}\right)$ and a continuous payoff $\left(x_{s}, s \leq T\right)$, where $x_{s}$ is paid at time $s$. Prove that the price of this claim is

\[V_{t}=\mathbb{E}_{\mathbb{Q}}\left(e^{-r(T-t)} h\left(S_{T}\right)+\int_{t}^{T} e^{-r(s-t)} x_{s} d s \mid \mathcal{F}_{t}\right)\]

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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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We consider a contingent claim with a terminal payoff (hleft(S_{T} ight)) and a continuous payoff (left(x_{s}, s

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Mathematical Methods For Financial Markets

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