In the mathematical theory of probability, a sigma-martingale is a semimartingale with an integral representation. Sigma-martingales were introduced by C.S. Chou and M. Emery in 1977 and 1978. 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).
Mathematical definition
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