Yan Theorem in L ∞ with Applications to Asset Pricing

Abstract

We prove an L ∞ version of Yan theorem and deduce from it a necessary condition for the absence of free lunches in a model of financial markets in which asset prices are a continuous R d valued process and only simple investment strategies are admissible. Our proof is based on a new separation theorem for convex sets of finitely additive measures.

The Kreps-Yan theorem for Banach ideal spaces

“…This result is established in [7, Theorem 2.1] (another independent proof was obtained in [9]). Note that the space l ∞ of bounded sequences which may be regarded as a Banach ideal space on the probability space (N, 2 N , Q), where Q(n) = 1/2 n is not weakly Lindelöf [10, Example 4.1(i)].…”

The Kreps‐Yan theorem for L∞

“…and there exists an element µ ∈ C • such that After the paper was submitted, Professor G. Cassese informed the author that he (by another methods) had independently and simultaneously proved a somewhat more general version of Theorem 2.1 [2]. We find it convenient to restate here the main ingredient of this approach together with its simple proof, based on Theorem 2.1.…”

“…We find it convenient to restate here the main ingredient of this approach together with its simple proof, based on Theorem 2.1. It should be mentioned that the argumentation of [2] goes in the opposite direction. Another interesting comment comes from Professor W. Schachermayer, who in a personal communication pointed out that the above ideas can be transformed in a more direct proof of Theorem 2.1.…”

Two versions of the fundamental theorem of asset pricing

“…Hence, a question is what happens if the closure is taken in the norm-topology, that is, if (a*) is replaced by (a). The answer, due to [8,Theorem 2] and [17, Theorem 2.1], is reported in Theorem 2.…”