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|
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- 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.
- 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.
- Jan Ericsson & Olivier Renault, 2006.
"Liquidity and Credit Risk,"
Journal of Finance,
American Finance Association, vol. 61(5), pages 2219-2250, October.
- 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.
- Instefjord, Norvald, 2005. "Risk and hedging: Do credit derivatives increase bank risk?," Journal of Banking & Finance, Elsevier, vol. 29(2), pages 333-345, February.
- Martens, Martin & van Dijk, Dick, 2007.
"Measuring volatility with the realized range,"
Journal of Econometrics,
Elsevier, vol. 138(1), pages 181-207, May.
- Fleten, Stein-Erik & Maribu, Karl Magnus & Wangensteen, Ivar, 2005.
"Optimal investment strategies in decentralized renewable power generation under uncertainty,"
218, University Library of Munich, Germany, revised Jun 2006.
- 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.
- He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 593-617.
- 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.
- 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.
- Ian Martin, 2011.
"The Lucas Orchard,"
NBER Working Papers
17563, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- 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.
- Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
- 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.
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