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

摘要

Let L be a linear space of real-bounded random variables on the probability space (Ω, A, P_0). A finitely additive probability P on A such that P～P_0 and E_p(X)=0 foreach X ∈ L is called equivalent martingale finitely additive probability (EMFA). In this paper, EMFAs are investigated in case P_0 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 y ∈ R and Y be a bounded random variable. Then X_n + y → Y, for some sequence (X_n) {is contained in} L, provided EMFAs exist and E_p(Y) = y for each EMFA P.