Price uniqueness and fundamental theorem of asset pricing with finitely additive probabilities

Abstract

Let L be a linear space of real-bounded random variables on the probability space . A finitely additive probability P on such thatis called equivalent martingale finitely additive probability (EMFA). In this paper, EMFAs are investigated in case P0 is atomic. Existence of EMFAs is characterized and a question raised in Berti et al. (2012, J. Theoret. Probab. Available at http://economia.unipv.it/pagp/pagine_personali/prigo/arb.pdf) is answered. Some results of the following type are obtained as well. Let and Y be a bounded random variable. Then , for some sequence , provided EMFAs exist and for each EMFA P.