Second Fundamental Theorem of Asset Pricing. 4. R - XYZ

Biagini, Francesca (2010): Second Fundamental Theorem of Asset Pricing. 4. R - XYZ. In: Cont, Rama (ed.) : Encyclopedia of Quantitative Finance. Chichester [u.a.]: Wiley. pp. 1623-1628

Abstract

The second fundamental theorem of asset pricing concerns the mathematical characterization of the economic concept of market completeness for liquid and frictionless markets. The theorem establishes the mathematical necessary and sufficient conditions in order to guarantee that every contingent claim on the market can be duplicated with a portfolio of primitive assets. For finite asset economies, completeness (i.e., perfect replication of every claim on the market by admissible self-financing strategies) is equivalent to uniqueness of the equivalent martingale measure. This result can be extended to market models with an infinite number of assets by defining completeness in terms of approximate replication of claims by attainable ones.

• Item Type: Book Section
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISBN: 978-0-470-06160-2 ; 978-0-470-05756-8
• Place of Publication: Chichester [u.a.]
• Language: English