Abstract
This paper is aimed at showing how prices can have the martingale property (MP) even when arbitrage opportunities exist. It is first recalled that arbitrage opportunities can be introduced if one suppose that some (few) Arrow-Debreu securities do not increase agents’ preferences. Viability can indeed be defined with this kind of preferences and pricing measures still exist but may be signed. Then because MP only relies on the absence of some conditional cash and carry arbitrages, we show that prices can still have MP under any of these so called signed measure. An analysis of a family of processes that have MP under a signed measure is set up. Such a study reveals an interesting phenomenology, qualitatively close to some stylized facts of financial markets.
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