A Simple Characterization of Dynamic Completeness in Continuous Time
This paper examines if (and how) continuous-time trading renders dynamically-complete a financial market in which the underlying risk process is a Brownian motion and the securities pay dividends that are proportional to geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, has been established recently in the literature for the case in which the financial market in question is part of a single-commodity, pure-exchange economy with many heterogenous agents, where all intermediate flows of utilities and endowments are analytic functions. The present paper shows that the condition is indeed sufficient, as well as necessary in some important cases, by means of a very different (and more intuitive) mathematical argument that assumes neither analyticity nor a particular economic environment. It requires only that the pricing kernels are continuous and satisfy a standard growth condition. In this sense, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.).
|Date of creation:||20 May 2012|
|Date of revision:||02 Sep 2013|
|Contact details of provider:|| Postal: |
Phone: 01334 462420
Fax: 01334 462444
Web page: http://www.st-andrews.ac.uk/economics/
More information through EDIRC
|Order Information:|| Email: |
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.:
- Ian Martin, 2013.
"The Lucas Orchard,"
Econometric Society, vol. 81(1), pages 55-111, 01.
- Cadenillas, Abel & Zapatero, Fernando, 1999. "Optimal Central Bank Intervention in the Foreign Exchange Market," Journal of Economic Theory, Elsevier, vol. 87(1), pages 218-242, July.
- Janis M. Carey & David Zilberman, 2002. "A Model of Investment under Uncertainty: Modern Irrigation Technology and Emerging Markets in Water," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 84(1), pages 171-183.
- Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
- J. Hugonnier & S. Malamud & E. Trubowitz, 2012.
"Endogenous Completeness of Diffusion Driven Equilibrium Markets,"
Econometric Society, vol. 80(3), pages 1249-1270, 05.
- Julien HUGONNIER & Semyon MALAMUD & Eugene TRUBOWITZ, . "Endogenous completeness of diffusion driven equilibrium markets," Swiss Finance Institute Research Paper Series 09-41, Swiss Finance Institute.
- Martens, M.P.E. & van Dijk, D.J.C., 2006.
"Measuring volatility with the realized range,"
Econometric Institute Research Papers
EI 2006-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Olivier Renault & Jan Ericsson, 2000.
"Liquidity and Credit Risk,"
FMG Discussion Papers
dp362, Financial Markets Group.
- Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
- Fleten, Stein-Erik & Maribu, Karl Magnus & Wangensteen, Ivar, 2005. "Optimal investment strategies in decentralized renewable power generation under uncertainty," MPRA Paper 218, University Library of Munich, Germany, revised Jun 2006.
- Epaulard, Anne & Pommeret, Aude, 2003. "Optimally eating a stochastic cake: a recursive utility approach," Resource and Energy Economics, Elsevier, vol. 25(2), pages 129-139, May.
- Basak, Suleyman & Cuoco, Domenico, 1998. "An Equilibrium Model with Restricted Stock Market Participation," Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 309-41.
- Instefjord, Norvald, 2005. "Risk and hedging: Do credit derivatives increase bank risk?," Journal of Banking & Finance, Elsevier, vol. 29(2), pages 333-345, February.
- Fleten, S.-E. & Maribu, K.M. & Wangensteen, I., 2007. "Optimal investment strategies in decentralized renewable power generation under uncertainty," Energy, Elsevier, vol. 32(5), pages 803-815.
- Postali, Fernando A.S. & Picchetti, Paulo, 2006. "Geometric Brownian Motion and structural breaks in oil prices: A quantitative analysis," Energy Economics, Elsevier, vol. 28(4), pages 506-522, July.
- He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 593-617.
- Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
- Bick, Avi, 1987. "On the Consistency of the Black-Scholes Model with a General Equilibrium Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 259-275, September.
- Farhi, Emmanuel & Panageas, Stavros, 2007. "Saving and investing for early retirement: A theoretical analysis," Journal of Financial Economics, Elsevier, vol. 83(1), pages 87-121, January.
When requesting a correction, please mention this item's handle: RePEc:san:wpecon:1312. 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: (Bram Boskamp)
If references are entirely missing, you can add them using this form.