 Martingale transfer under a density process (source code)

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= Martingale transfer under a density process

Let $Z$ be a positive uniformly integrable martingale defining $d\widetilde{\mathbb P}=Z_\infty\,d\mathbb P$. If $Y$ is bounded and $ZY$ is a true $\mathbb P$-martingale, then $Y$ is a $\widetilde{\mathbb P}$-martingale. This follows from the conditional-expectation change-of-measure identity.

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