A Benchmark Approach to Investing and Pricing

Eckhard Platen ()

No 253, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper introduces a general market modeling framework, the benchmark approach, which assumes the existence of the numeraire portfolio. This is the strictly positive portfolio that when used as benchmark makes all benchmarked nonnegative portfolios supermartingales, that is intuitively speaking downward trending or trendless. It can be shown to equal the Kelly portfolio which maximizes expected logarithmic utility. In several ways the Kelly or numeraire portfolio is the "best" performing portfolio and can not be out performed systematically by any other nonnegative portfolio. Its use in pricing as numeraire leads directly to the real world pricing formula, which employs the real world probability when calculating conditional expectations. In a large regular financial market, the Kelly portfolio is shown to be approximated by well diversified portfolios.

Keywords: Kelly portfolio; real world pricing; numeraire portfolio; strong arbitrage; diversification (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2009-08-01
New Economics Papers: this item is included in nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Published as: Platen, E., 2011, "A Benchmark Approach to Investing and Pricing", In: The Kelly Capital Growth Investment Criterion: Theory and Practice, 409-426.

Downloads: (external link)
https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp253.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp253.pdf [301 Moved Permanently]--> https://www.uts.edu.au/globalassets/sites/default/files/qfr-archive-03/QFR-rp253.pdf)

Related works:
Chapter: A Benchmark Approach to Investing and Pricing (2011)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:uts:rpaper:253

Access Statistics for this paper

More papers in Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Duncan Ford ().