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When deriving the rough Bergomi model, Bayer et al in "Pricing Under Rough Volatility" (2015) perform a change of measure to ensure the price process is a martingale as shown in the screenshot below:

Bayer change of measure

However, there is recent academic work, such as the "On the martingale property in the rough Bergomi model" by Gassiat in 2019, showing that the process is a local martingale and a true martingale under certain conditions as shown in the screenshot below:

current work on martingale properties

I don't understand how, under the risk neutral measure, the price process is a martingale and yet current work says it's an unanswered question.

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  • $\begingroup$ In the Bayer paper, the time domain is $[0,T]$, so any local Martingale is a Martingale. However, in Gassiat, the domain is $[0, \infty)$. Does that resolve your problem? $\endgroup$
    – Achrbot
    Commented Jul 17, 2023 at 12:44

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