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No Arbitrage and General Semimartingales

Philip E. Protter, Kazuhiro Shimbo

Open publisher page 101 citations

Abstract

<!-- *** Custom HTML *** --> No free lunch with vanishing risk (NFLVR) is known to be equivalent to the existence of an equivalent martingale measure for the price process semimartingale. We give necessary conditions for such a semimartingale to have the property NFLVR. We also extend Novikov’s criterion for the stochastic exponential of a local martingale to be a martingale to the general case; that is, the case where the paths need not be continuous.

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What this paper is about

<!-- *** Custom HTML *** --> No free lunch with vanishing risk (NFLVR) is known to be equivalent to the existence of an equivalent martingale measure for the price process semimartingale. We give necessary conditions for such a semimartingale to have the property NFLVR. We also extend Novikov’s criterion for the stochastic exponential of a local martingale to be a martingale to the general case; that is, the case where the paths need not be continuous.

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OpenAlex reports 101 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

<!-- *** Custom HTML *** --> No free lunch with vanishing risk (NFLVR) is known to be equivalent to the existence of an equivalent martingale measure for the price process semimartingale. We give necessary conditions for such a semimartingale to have the property NFLVR. We also extend Novikov’s criterion for the stochastic exponential of a local martingale to be a martingale to the general case; that is, the case where the paths need not be continuous.

Key concepts: Semimartingale, Local martingale, Martingale (probability theory), Mathematics, Novikov self-consistency principle, Martingale pricing, Arbitrage, Mathematical economics

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