The Fundamental Theorem of Asset Pricing for Self-Financing Portfolios

Eckhard Platen () and Stefan Tappe

No 411, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: Consider a financial market with nonnegative semimartingales which does not need to have a numéraire. We are interested in the absence of arbitrage in the sense that no self-financing portfolio gives rise to arbitrage opportunities, where we are allowed to add a savings account to the market. We will prove that in this sense the market is free of arbitrage if and only if there exists an equivalent local martingale deator which is a multiplicative special semimartingale. In this case, the additional savings account relates to the finite variation part of the multiplicative decomposition of the deflator. By focusing on self-financing portfolios, this result clarifies links between previous results in the literature and makes the respective concepts more realistic.

Keywords: fundamental theorem of asset pricing; self-financing portfolio, noarbitrage concept; equivalent local martingale deflator (search for similar items in EconPapers)
Pages: 34 pages
Date: 2020-05-01
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Citations: View citations in EconPapers (2)

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