The absence of arbitrages of the first kind, a weakening of the " No Free Lunch with Vanishing Risk " condition, is analyzed in a general semimartingale financial market model. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP) , it is shown that there is  absence of arbitrages of the first kind in the market if and only if an equivalent local martingale deflator (ELMD) exists. An ELMD is a strictly positive process that , when deflated by it, discounted nonnegative wealth processes become local martingales. In terms of measures, absence of arbitrages of the first kind is shown to be equivalent to the existence of a finitely additive probability, weakly equivalent to the original and locally countably additive, under which the discounted asset-price process is a "local martingale ". Finally, the aforementioned results are used to obtain an independent proof of the FTAP .
The absence of arbitrages of the first kind, a weakening of the `` No Free Lunch with Vanishing Risk '' condition, is analyzed in a general semimartingale financial market model. In the spirit of the Fundamental Theorem of Asset Pricing , it is shown that there is equivalence between the absence of arbitrages of the first kind and the existence of a strictly positive process that acts as a local martingale deflator on nonnegative wealth processes .
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equivalence between the
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in the market if and only if an equivalent local martingale deflator (ELMD) exists. An ELMD is
and the existence of
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, when deflated by it, discounted nonnegative wealth processes become local martingales. In terms of measures, absence of arbitrages of the first kind is shown to be equivalent to the existence of a finitely additive probability, weakly equivalent to the original and locally countably additive, under which the discounted asset-price process is a "local martingale ". Finally, the aforementioned results are used to obtain an independent proof of the FTAP
acts as a local martingale deflator on nonnegative wealth processes