M6 - On Minimal Market Models and Minimal Martingale Measures
The well-known absence-of-arbitrage condition NFLVR from the fundamental theorem of asset pricing splits into two conditions, called NA and NUPBR. We give a literature overview of several equivalent reformulations of NUPBR; these include existence of a growth-optimal portfolio, existence of the numeraire portfolio, and for continuous asset prices the structure condition (SC). As a consequence, the minimal market model of E. Platen is seen to be directly linked to the minimal martingale measure. We then show that reciprocals of stochastic exponentials of continuous local martingales are time changes of a squared Bessel process of dimension 4. This directly gives a very specific probabilistic structure for minimal market models.
|Date of creation:||01 Jun 2010|
|Publication status:||Published as: Hulley, H. and Schweizer, M., 2010, "M6 - On Minimal Market Models and Minimal Martingale Measures", In: Carl Chiarella and Alexander Novikov (eds) Contemporary Quantitative Finance: Essays in Honour of Eckhard Platen, 35-51.|
|Contact details of provider:|| Postal: PO Box 123, Broadway, NSW 2007, Australia|
Phone: +61 2 9514 7777
Fax: +61 2 9514 7711
Web page: http://www.qfrc.uts.edu.au/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
- Eva Strasser, 2005. "Characterization of arbitrage-free markets," Papers math/0503473, arXiv.org.
- Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
- Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series 103, Quantitative Finance Research Centre, University of Technology, Sydney.
- Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Eckhard Platen, 2004.
"Diversified Portfolios with Jumps in a Benchmark Framework,"
Asia-Pacific Financial Markets,
Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
- Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney.
- Michel Chatelain & Christophe Stricker, 1994. "ON COMPONENTWISE and VECTOR STOCHASTIC INTEGRATION," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 57-65.
- Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, September. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:280. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford)
If references are entirely missing, you can add them using this form.