Finite horizon arbitrage-free security markets

This paper studies the weakly and strictly arbitrage-free security markets. The authors extend the Farkas-Minkowski's Lemma and Stiemke's Lemma from two periods to finite periods and from finite-dimensional (Euclidean) space to locally convex topological space and separable Banach space, show weakly and strictly arbitrage-free security pricing theory, then obtain the conditional expectation form of weakly and strictly arbitrage-free security pricing formula.