On Financial Markets where only Buy-And-Hold Trading is Possible
AbstractA 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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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 213.
Date of creation: 01 Feb 2008
Date of revision:
numeraire portfolio; semimartingales; buy-and-hold strategies; unbounded profit with bounded risk; supermartingale deflators; utility maximization.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-03-08 (All new papers)
- NEP-FMK-2008-03-08 (Financial Markets)
- NEP-UPT-2008-03-08 (Utility Models & Prospect Theory)
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