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Sigma-martingale : ウィキペディア英語版
Sigma-martingale

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 ==
An \mathbb^d-valued stochastic process X = (X_t)_^T is a ''sigma-martingale'' if it is a semimartingale and there exists an \mathbb^d-valued martingale ''M'' and an ''M''-integrable predictable process \phi with values in \mathbb_+ such that
:X = \phi \cdot M. \,

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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