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2015 Two versions of the fundamental theorem of asset pricing
Patrizia Berti, Luca Pratelli, Pietro Rigo
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Electron. J. Probab. 20: 1-21 (2015). DOI: 10.1214/EJP.v20-3321

Abstract

Let $L$ be a convex cone of real random variables on the probability space $(\Omega,\mathcal{A},P_0)$. The existence of a probability $P$ on $\mathcal{A}$ such that $\begin{equation*} P \sim P_0,\quad E_P\left|X\right| < \infty\,\textrm{and} E_P(X)\leq 0\, \mathrm{for all} X \in L \end{equation*}$ is investigated. Two results are provided. In the first, $P$ is a finitely additive probability, while $P$ is $\sigma$-additive in the second. If $L$ is a linear space then $-X\in L$ whenever $X \in L$, so that $E_P(X)\leq 0$ turns into $E_P(X)=0$. Hence, the results apply to various significant frameworks, including equivalent martingale measures and equivalent probability measures with given marginals.

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Patrizia Berti. Luca Pratelli. Pietro Rigo. "Two versions of the fundamental theorem of asset pricing." Electron. J. Probab. 20 1 - 21, 2015. https://doi.org/10.1214/EJP.v20-3321

Information

Accepted: 29 March 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1326.60007
MathSciNet: MR3335825
Digital Object Identifier: 10.1214/EJP.v20-3321

Subjects:
Primary: 60A05
Secondary: 28C05, 60A10, 91B25, 91G10

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