Compactness Criterion for Semimartingale Laws and Semimartingale Optimal Transport

10 May 2018 Liu Chong Neufeld Ariel

We provide a compactness criterion for the set of laws $\mathfrak{P}^{ac}_{sem}(\Theta)$ on the Skorokhod space for which the canonical process $X$ is a semimartingale having absolutely continuous characteristics with differential characteristics taking values in some given set $\Theta$ of L\'evy triplets. Whereas boundedness of $\Theta$ implies tightness of $\mathfrak{P}^{ac}_{sem}(\Theta)$, closedness fails in general, even when choosing $\Theta$ to be additionally closed and convex, as a sequence of purely discontinuous martingales may converge to a diffusion... (read more)

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