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On the semimartingale property of discounted asset-price processes

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  • Constantinos Kardaras
  • Eckhard Platen

Abstract

A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a natural market viability assumption, namely, absence of arbitrages of the first kind, we establish that discounted asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves strictly positive supermartingale deflators rather than Equivalent Martingale Measures.

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File URL: http://arxiv.org/pdf/0803.1890
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0803.1890.

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Date of creation: Mar 2008
Date of revision: Nov 2009
Handle: RePEc:arx:papers:0803.1890

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References

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  1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
  2. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
  3. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
  4. Robert Fernholz & Ioannis Karatzas & Constantinos Kardaras, 2005. "Diversity and relative arbitrage in equity markets," Finance and Stochastics, Springer, vol. 9(1), pages 1-27, January.
  5. Constantinos Kardaras, 2010. "Numéraire-invariant preferences in financial modeling," LSE Research Online Documents on Economics 44993, London School of Economics and Political Science, LSE Library.
  6. Kasper Larsen & Gordan Žitković, 2008. "On the semimartingale property via bounded logarithmic utility," Annals of Finance, Springer, vol. 4(2), pages 255-268, March.
  7. Erhan Bayraktar & Hasanjan Sayit, 2010. "No arbitrage conditions for simple trading strategies," Annals of Finance, Springer, vol. 6(1), pages 147-156, January.
  8. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. repec:wop:humbsf:1997-31 is not listed on IDEAS
  10. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July.
  11. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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Cited by:
  1. Constantinos Kardaras & Eckhard Platen, 2008. "Minimizing the Expected Market Time to Reach a Certain Wealth Level," Research Paper Series 230, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Constantinos Kardaras, 2013. "On the closure in the Emery topology of semimartingale wealth-process sets," LSE Research Online Documents on Economics 44996, London School of Economics and Political Science, LSE Library.
  3. Mathias Beiglb\"ock & Walter Schachermayer & Bezirgen Veliyev, 2010. "A Direct Proof of the Bichteler--Dellacherie Theorem and Connections to Arbitrage," Papers 1004.5559, arXiv.org.
  4. Constantinos Kardaras, 2009. "Finitely additive probabilities and the Fundamental Theorem of Asset Pricing," Papers 0911.5503, arXiv.org.
  5. Constantinos Kardaras & Eckhard Platen, 2008. "Multiplicative approximation of wealth processes involving no-short-sale strategies via simple trading," Papers 0812.0033, arXiv.org, revised Mar 2010.
  6. Constantinos Kardaras, 2011. "On the closure in the Emery topology of semimartingale wealth-process sets," Papers 1108.0945, arXiv.org, revised Jul 2013.
  7. Leunglung Chan & Eckhard Platen, 2010. "Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model," Papers 1007.2968, arXiv.org, revised Jan 2011.

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