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On Financial Markets where only Buy-And-Hold Trading is Possible


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A financial market model where agents can only trade using realistic buyand-hold strategies is considered. Minimal assumptions are made on the nature of the asset-price process — in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have to be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Martingale Measures. Further, the utility maximization problem is considered and it is shown that using only buy-and-hold strategies, optimal utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 213.

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Length: 24
Date of creation: 01 Feb 2008
Date of revision:
Handle: RePEc:uts:rpaper:213

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Keywords: numeraire portfolio; semimartingales; buy-and-hold strategies; unbounded profit with bounded risk; supermartingale deflators; utility maximization.;

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  1. repec:wop:humbsf:1997-31 is not listed on IDEAS
  2. 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. Eckhard Platen & Renata Rendek, 2010. "Approximating the Numeraire Portfolio by Naive Diversification," Research Paper Series 281, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Constantinos Kardaras, 2008. "The continuous behavior of the numeraire portfolio under small changes in information structure, probabilistic views and investment constraints," Papers 0804.2912,, revised Nov 2009.
  4. Eckhard Platen, 2009. "A Benchmark Approach to Investing and Pricing," Research Paper Series 253, Quantitative Finance Research Centre, University of Technology, Sydney.


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