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State Tameness: A New Approach for Credit Constrains


  • Jaime A. Londo~no


We 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.

Suggested Citation

  • Jaime A. Londo~no, 2003. "State Tameness: A New Approach for Credit Constrains," Papers math/0305274,, revised Feb 2004.
  • Handle: RePEc:arx:papers:math/0305274

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    References listed on IDEAS

    1. 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.
    2. repec:arz:wpaper:eres1993-121 is not listed on IDEAS
    3. 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.
    4. 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.
    5. 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.
    6. Peter Lakner, 1993. "Martingale Measures For A Class of Right-Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 43-53.
    7. Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
    8. Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130.
    9. 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.
    10. Willard, Gregory A & Dybvig, Philip H, 1999. "Empty Promises and Arbitrage," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 807-834.
    11. 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.
    12. Hindy, Ayman, 1995. "Viable prices in financial markets with solvency constraints," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 105-135.
    13. 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 1219-1235.
    14. 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 1211-1250.
    15. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
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    Cited by:

    1. Jaime A. Londo~no, 2005. "Dynamic State Tameness," Papers math/0509139,
    2. Jaime A. Londo~no, 2006. "State Dependent Utility," Papers math/0603316,
    3. Jaime LondoƱo, 2005. "Dynamic State Tameness," Finance 0509010, EconWPA, revised 20 Sep 2005.

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