Risk-neutral valuation with infinitely many trading dates

Authors:
Alejandro BalbáS;Raquel BalbáS;Silvia Mayoral
Affiliations:
Universidad Carlos III, CL, Madrid 126, 28903 Getafe, Madrid, Spain;Universidad Autónoma. Avda. Tomás y Valiente 5, Módulo E-XVI, 28049 Madrid, Spain;Universidad de Navarra, Edificio Bibliotecas, 31080 Pamplona, Navarra, Spain
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2007

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Abstract

The first Fundamental Theorem of Asset Pricing establishes the equivalence between the absence of arbitrage in financial markets and the existence of Equivalent Martingale Measures, if appropriate conditions hold. Since the theorem may fail when dealing with infinitely many trading dates, this paper draws on the A.A. Lyapunov Theorem in order to retrieve the equivalence for complete markets such that the Sharpe Ratio is adequately bounded.