Arbitrage-Free Asset Pricing in General State Space

Xiaotie Deng, Shunming Zhang

Abstract: This paper studies asset pricing in abitrage-free financial markets in general state space. The mathematical formulation is based on a locally convex topological space for weakly arbitrage-free securities’ structure and a separable Banach space for strictly arbitrage-free securities’ structure. We establish, for these two types of spaces, the weakly arbitrage-free pricing theorem and the strictly arbitrage-free pricing theorem, respectively.