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

Constantinos Kardaras and Eckhard Platen ()

No 213, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: 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.

Keywords: numeraire portfolio; semimartingales; buy-and-hold strategies; unbounded profit with bounded risk; supermartingale deflators; utility maximization. (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fmk and nep-upt
Date: 2008-02-01
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