Finitely Additive FTAP under an Atomic Reference Measure
نویسندگان
چکیده
Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). A finitely additive probability P on A such that P ∼ P0 and EP (X) = 0 for each X ∈ L is called EMFA (equivalent martingale finitely additive probability). In this note, EMFA’s are investigated in case P0 is atomic. Existence of EMFA’s is characterized and various examples are given. Given y ∈ R and a bounded random variable Y , it is also shown that Xn + y a.s. −→ Y , for some sequence (Xn) ⊂ L, provided EMFA’s exist and EP (Y ) = y for each EMFA P .
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Price Uniqueness and Ftap with Finitely Additive Probabilities
Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). A finitely additive probability P on A such that P ∼ P0 and EP (X) = 0 for each X ∈ L is called EMFA (equivalent martingale finitely additive probability). In this paper, EMFA’s are investigated in case P0 is atomic. Existence of EMFA’s is characterized and a question raised in [3] is answered. Some res...
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