State Tameness: A New Approach for Credit Constrains
AbstractWe propose a new definition for tameness within the model of security prices as It\^o processes that is risk-aware. We give a new definition for arbitrage and characterize it. We then prove a theorem that can be seen as an extension of the second fundamental theorem of asset pricing, and a theorem for valuation of contingent claims of the American type. The valuation of European contingent claims and American contingent claims that we obtain does not require the full range of the volatility matrix. The technique used to prove the theorem on valuation of American contingent claims does not depend on the Doob-Meyer decomposition of super-martingales; its proof is constructive and suggest and alternative way to find approximations of stopping times that are close to optimal.
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.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number math/0305274.
Date of creation: May 2003
Date of revision: Feb 2004
Publication status: Published in Electronic Communications in Probability, 9, (2004), 1-13
Contact details of provider:
Web page: http://arxiv.org/
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.:
- Battig, Robert J & Jarrow, Robert A, 1999. "The Second Fundamental Theorem of Asset Pricing: A New Approach," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1219-35.
- Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
- Willard, Gregory A & Dybvig, Philip H, 1999. "Empty Promises and Arbitrage," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 807-34.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130.
- Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-50.
- Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
- Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
- Peter Lakner, 1993. "Martingale Measures For A Class of Right-Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 43-53.
- Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
- Robert A. Jarrow & Dilip B. Madan, 1991. "A Characterization of Complete Security Markets On A Brownian Filtration," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 31-43.
- Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- Jaime A. Londo\~no, 2005. "Dynamic State Tameness," Papers math/0509139, arXiv.org.
- Jaime Londoño, 2005. "Dynamic State Tameness," Finance 0509010, EconWPA, revised 20 Sep 2005.
- Jaime A. Londo\~no, 2006. "State Dependent Utility," Papers math/0603316, arXiv.org.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.