TITLE:
The Fundamental Theorem of Asset Pricing with either Frictionless or Frictional Security Markets
AUTHORS:
Helen H. Huang, Shunming Zhang
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
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.4 No.2,
February
27,
2014
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.