Finitely additive probabilities and the Fundamental Theorem of Asset Pricing
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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| Date of creation: | Nov 2009 |
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| Handle: | RePEc:arx:papers:0911.5503 |
| Contact details of provider: | Web page: http://arxiv.org/
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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Eckhard Platen, 2006.
"A Benchmark Approach To Finance,"
Mathematical Finance,
Wiley Blackwell, vol. 16(1), pages 131-151.
- Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
- Loewenstein, Mark & Willard, Gregory A., 2000. "Rational Equilibrium Asset-Pricing Bubbles in Continuous Trading Models," Journal of Economic Theory, Elsevier, vol. 91(1), pages 17-58, March.
- (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
- Kardaras, Constantinos & Platen, Eckhard, 2011.
"On the semimartingale property of discounted asset-price processes,"
Stochastic Processes and their Applications,
Elsevier, vol. 121(11), pages 2678-2691, November.
- Constantinos Kardaras & Eckhard Platen, 2008. "On the semimartingale property of discounted asset-price processes," Papers 0803.1890, arXiv.org, revised Nov 2009.
- Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
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