Finitely additive probabilities and the Fundamental Theorem of Asset Pricing

Details Finitely additive probabilities and the Fundamental Theorem of Asset Pricing Finitely additive probabilities and the Fundamental Theorem of Asset Pricing

2009-11-29

arxiv.org/abs/0911.5503v1

Economy

Quantitative Finance

Pricing of Securities

14 pages. Dedicated to Prof. Eckhard Platen, on the occasion of his 60th birthday. This is the 2nd part of what comprised the

Scientific paper

This work aims at a deeper understanding of the mathematical implications of the economically-sound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that absence of arbitrages of the first kind in the market is equivalent to the existence of a finitely additive probability, weakly equivalent to the original and only locally countably additive, under which the discounted wealth processes become "local martingales". The aforementioned result is then used to obtain an independent proof of the FTAP of Delbaen and Schachermayer. Finally, an elementary and short treatment of the previous discussion is presented for the case of continuous-path semimartingale asset-price processes.

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