Two versions of the fundamental theorem of asset pricing

@inproceedings{Berti2014TwoVO,
  title={Two versions of the fundamental theorem of asset pricing},
  author={Patrizia Berti and Luca Pratelli and Pietro Rigo},
  year={2014}
}
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 $$ P \sim P_0,\quad E_P \abs{X}< \infty\, \text{ and } \, E_P(X) \leq 0\, \text{ for all }X \in L $$ 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… CONTINUE READING

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