Weak measurability and characterizations of risk
AbstractIn the context of a continuum of random variables, arising, for example, as rates of return in financial markets with a continuum of assets, or as individual responses in games with a continuum of players, an important economic issue is to show how idiosyncratic risk can be removed through some device of aggregation or diversification when such risk is explicitly introduced into the model. In this paper, we use recent work of Al-Najjar  as a general backdrop to provide a review of the basic issues involved when the continuum is formulated as the Lebesgue interval. We present two examples to argue that the fundamental problem of the non-measurability of sample functions, originally identified by Doob, and further elaborated by Feldman, Gilles and Judd in the economic literature, simply cannot be bypassed by reinterpretations of standard results. We also provide an equivalence result in the spirit of Al-Najjar's efforts; but argue that this elementary result does not go beyond the standard law of large numbers for a sequence of real-valued iid random variables, and as such, is incapable of yielding anything of substantive economic interest beyond this law.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Springer in its journal Economic Theory.
Volume (Year): 13 (1999)
Issue (Month): 3 ()
Note: Received: April 23, 1998; revised version: April 28, 1998
Contact details of provider:
Web page: http://link.springer.de/link/service/journals/00199/index.htm
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- M Ali Khan & Yeneng Sun, 2002.
"Exact Arbitrage and Portfolio Analysis in Large Asset Markets,"
Economics Working Paper Archive
484, The Johns Hopkins University,Department of Economics.
- M. Ali Khan & Yeneng Sun, 2003. "Exact arbitrage and portfolio analysis in large asset markets," Economic Theory, Springer, vol. 22(3), pages 495-528, October.
- Khan, M. Ali & Sun, Yeneng, 2003.
"Exact arbitrage, well-diversified portfolios and asset pricing in large markets,"
Journal of Economic Theory,
Elsevier, vol. 110(2), pages 337-373, June.
- Khan, M. Ali & Sun, Yeneng, 2001. "Exact Arbitrage, Well-Diversified Portfolios and Asset Pricing in Large Markets," Economics Working Papers (Ensaios Economicos da EPGE) 420, Graduate School of Economics, Getulio Vargas Foundation (Brazil).
- M Ali Khan & Yeneng Sun, 2002. "Exact Arbitrage Well-Diversified Potfolios and Asset Pricing in Large Markets," Economics Working Paper Archive 483, The Johns Hopkins University,Department of Economics.
- Peter Hammond & Yeneng Sun, 2001.
"Monte Carlo Simulation of Macroeconomic Risk with a Continuum of Agents: The Symmetric Case,"
01015, Stanford University, Department of Economics.
- Peter J. Hammond & Yeneng Sun, 2003. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case," Economic Theory, Springer, vol. 21(2), pages 743-766, 03.
- Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
- Khan, A. & Sun, Y., 2000.
"Asymptotic Arbitrage and the APT with or Without Measure-Theoretic Structures,"
Papiers d'Economie MathÃÂ©matique et Applications
2000.81, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Khan, M. Ali & Sun, Yeneng, 2001. "Asymptotic Arbitrage and the APT with or without Measure-Theoretic Structures," Journal of Economic Theory, Elsevier, vol. 101(1), pages 222-251, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
If references are entirely missing, you can add them using this form.