In mathematics and information theory of probability, a sigma-martingale is a semimartingale with an integral representation.
[1] In financial mathematics, sigma-martingales appear in the fundamental theorem of asset pricing as an equivalent condition to no free lunch with vanishing risk (a no-arbitrage condition).
is a sigma-martingale if it is a semimartingale and there exists an
-valued martingale M and an M-integrable predictable process
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