Finitely Additive Equivalent Martingale Measures
نویسندگان
چکیده
Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L, if and only if c EQ(X) ≤ ess sup(−X), X ∈ L, for some constant c > 0 and (countably additive) probability Q on A such that Q ∼ P0. A necessary condition for such a P to exist is L − L+∞ ∩ L + ∞ = {0}, where the closure is in the norm-topology. If P0 is atomic, the condition is sufficient as well. In addition, there is a finitely additive probability P on A, such that P ≪ P0 and EP (X) = 0 for all X ∈ L, if and only if ess sup(X) ≥ 0 for all X ∈ L.
منابع مشابه
Finitely Additive Equivalent
Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L, if and only if c EQ(X) ≤ ess sup(−X), X ∈ L, for some constant c > 0 and (countably additive) probability Q on A such that Q ∼ P0. A necessary condition for such a P to exist is L− L∞ ∩ L∞ = {0}, where the cl...
متن کاملMartingale Pricing Measures in Incomplete Markets via Stochastic Programming Duality in the Dual of L
We propose a new framework for analyzing pricing theory for incomplete markets and contingent claims, using conjugate duality and optimization theory. Various statements in the literature of the fundamental theorem of asset pricing give conditions under which an essentially arbitrage-free market is equivalent to the existence of an equivalent martingale measure, and a formula for the fair price...
متن کاملTwo versions of the fundamental theorem of asset pricing
Let L be a convex cone of real random variables on the probability space (Ω,A, P0). The existence of a probability P on A such that P ∼ P0, EP |X| <∞ and EP (X) ≤ 0 for all X ∈ L is investigated. Two types of results are provided, according to P is finitely additive or σ-additive. The main results concern the latter case (i.e., P is a σ-additive probability). If L is a linear space then −X ∈ L ...
متن کاملPrice 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...
متن کاملFinitely Additive FTAP under an Atomic Reference Measure
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 b...
متن کامل