Price Uniqueness and Ftap with Finitely Additive Probabilities

Finitely 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...

Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach

We study the information that a distribution function provides about the finitely additive probability measure inducing it. We show that in general there is an infinite number of finitely additive probabilities associated with the same distribution function. Secondly, we investigate the relationship between a distribution function and its given sequence of moments. We provide formulae for the s...

The Foundations of Probability with Black Swans

We extend the foundation of probability in samples with rare events that are potentially catastrophic, called black swans, such as natural hazards, market crashes, catastrophic climate change, and species extinction. Such events are generally treated as “outliers” and disregarded. We propose a new axiomatization of probability requiring equal treatment in the measurement of rare and frequent ev...

Decomposition of group-valued measures on orthoalgebras

We present a general decomposition theorem for a positive inner regular finitely additive measure on an orthoalgebra L with values in an ordered topological group G, not necessarily commutative. In the case where L is a Boolean algebra, we establish the uniqueness of such a decomposition. With mild extra hypotheses on G, we extend this Boolean decomposition, preserving the uniqueness, to the ca...

Representing Finitely Additive Invariant Probabilities