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On the semimartingale property of discounted asset-price processes

  • Kardaras, Constantinos
  • Platen, Eckhard

A financial market model where agents trade using realistic combinations of simple (i.e., finite combinations of buy-and-hold) no-short-sales 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 arbitrage of the first kind, we establish that discounted asset-prices have to be semimartingales. Our main result can also be regarded as reminiscent of the Fundamental Theorem of Asset Pricing.

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Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 121 (2011)
Issue (Month): 11 (November)
Pages: 2678-2691

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Handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2678-2691
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  1. 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.
  2. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
  3. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
  4. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
  5. 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.
  6. 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.
  7. 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.
  8. Erhan Bayraktar & Hasanjan Sayit, 2010. "No arbitrage conditions for simple trading strategies," Annals of Finance, Springer, vol. 6(1), pages 147-156, January.
  9. Kasper Larsen & Gordan Žitković, 2008. "On the semimartingale property via bounded logarithmic utility," Annals of Finance, Springer, vol. 4(2), pages 255-268, March.
  10. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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