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Exponentially affine martingales, affine measure changes and exponential moments of affine processes

  • Kallsen, Jan
  • Muhle-Karbe, Johannes
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    We consider local martingales of exponential form or , where X denotes one component of a multivariate affine process. We give a weak sufficient criterion for M to be a true martingale. As a first application, we derive a simple sufficient condition for absolute continuity of the laws of two given affine processes. As a second application, we study whether the exponential moments of an affine process solve a generalized Riccati equation.

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    File URL: http://www.sciencedirect.com/science/article/B6V1B-4XKHDDB-1/2/227003ea540e3cf57a1de642c14fd69d
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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 120 (2010)
    Issue (Month): 2 (February)
    Pages: 163-181

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    Handle: RePEc:eee:spapps:v:120:y:2010:i:2:p:163-181
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    1. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    3. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382.
    4. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    5. Li Chen & Damir Filipovic, 2003. "A Simple Model for Credit Migration and Spread Curves," Finance 0305003, EconWPA.
    6. Li Chen & Damir Filipović, 2005. "A simple model for credit migration and spread curves," Finance and Stochastics, Springer, vol. 9(2), pages 211-231, 04.
    7. Ernst Eberlein & Jean Jacod & Sebastian Raible, 2005. "Lévy term structure models: No-arbitrage and completeness," Finance and Stochastics, Springer, vol. 9(1), pages 67-88, January.
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