The Fundamental Theorem of Asset Pricing with either Frictionless or Frictional Security Markets

Helen H. Huang, Shunming Zhang

Faculty of Business Administration, The University of Regina, Regina, Canada.
School of Finance, Renmin University of China, Beijing, China.

DOI: 10.4236/jmf.2014.42012                

Abstract

This paper studies asset pricing in arbitrage-free financial markets in general state space (both for frictionless market and for market with transaction cost). 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.

Keywords

The First Fundamental Valuation Theorems; Transaction Costs; Weak Arbitrage-Freeness; Strict Arbitrage-Freeness; Arbitrage-Free Pricing Theory; Locally Convex Topological Space; Separable Banach Space

Conflicts of Interest

The authors declare no conflicts of interest.

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