Sure Wins, Separating Probabilities and the Representation of Linear Functionals

Abstract

We discuss conditions under which a convex cone $\K\subset \R^Ω$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely additive expectations. A version of Riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions

References in corpus (1)

• Supermartingale Deomposition with General Index Set

Cited by in corpus (6)

• Asset Pricing in an Imperfect World
• Convergence in measure under Finite Additivity
• Complete and competitive financial markets in a complex world
• The Theorem of Halmos and Savage under Finite Additivity
• Supermartingale Deomposition with General Index Set
• Conglomerability and Finitely Additive Representations