The Kreps-Yan theorem forL∞

The Kreps-Yan theorem for L∞

Let 〈X ,Y〉 be a pair of Banach spaces in separating duality [18, Chapter IV]. A convex set M ⊂ X is called cone if λx ∈M for any x ∈M, λ ≥ 0. A cone M is called pointed if M∩ (−M)= {0}. Suppose that X is endowed with a locally convex topology τ, which is always assumed to be compatible with the duality 〈X ,Y〉, and K ⊂ X is a τ-closed pointed cone. An element ξ ∈ Y is called strictly positive if...

Kreps-yan Theorem for Banach Ideal Spaces

Let C be a closed convex cone in a Banach ideal space X on a measurable space with a σ-finite measure. We prove that conditions C ∩ X+ = {0} and C ⊃ −X+ imply the existence of a strictly positive continuous functional on X , whose restriction to C is non-positive. Let (Ω,F ) be a measurable space, which is complete with respect to a measure (that is, a countably-additive function) μ : F 7→ [0,∞...

Yan Theorem in L∞ with Applications to Asset Pricing

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 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 Drell-Yan

No Arbitrage : On the Work of David Kreps

Since the seminal papers by Black, Scholes and Merton on the pricing of options (Nobel Prize for Economics, 1997), the theory of No Arbitrage plays a central role in Mathematical Finance. Pioneering work on the relation between no arbitrage arguments and martingale theory has been done in the late seventies by M. Harrison, D. Kreps and S. Pliska. In the present note we give a brief survey on th...