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A characterization of the martingale property of exponentially affine processes

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  • Mayerhofer, Eberhard
  • Muhle-Karbe, Johannes
  • Smirnov, Alexander G.

Abstract

We consider local martingales of exponential form or where X denotes one component of a multivariate affine process in the sense of Duffie et al. (2003) [8]. By completing the characterization of conservative affine processes in [8, Section 9], we provide deterministic necessary and sufficient conditions in terms of the parameters of X for M to be a true martingale.

Suggested Citation

  • Mayerhofer, Eberhard & Muhle-Karbe, Johannes & Smirnov, Alexander G., 2011. "A characterization of the martingale property of exponentially affine processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 568-582, March.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:3:p:568-582
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    References listed on IDEAS

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    1. Blei, Stefan & Engelbert, Hans-Jürgen, 2009. "On exponential local martingales associated with strong Markov continuous local martingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2859-2880, September.
    2. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    3. Kallsen, Jan & Muhle-Karbe, Johannes, 2010. "Exponentially affine martingales, affine measure changes and exponential moments of affine processes," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 163-181, February.
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    Cited by:

    1. Richter, Anja, 2014. "Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3578-3611.
    2. Ruf, Johannes, 2013. "A new proof for the conditions of Novikov and Kazamaki," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 404-421.
    3. Branger, Nicole & Muck, Matthias & Seifried, Frank Thomas & Weisheit, Stefan, 2017. "Optimal portfolios when variances and covariances can jump," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 59-89.
    4. Keller-Ressel, Martin, 2015. "Simple examples of pure-jump strict local martingales," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4142-4153.
    5. Hardy Hulley & Johannes Ruf, 2019. "Weak Tail Conditions for Local Martingales," Published Paper Series 2019-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    6. Mayerhofer, Eberhard & Stelzer, Robert & Vestweber, Johanna, 2020. "Geometric ergodicity of affine processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4141-4173.
    7. Martin Keller-Ressel, 2014. "Simple examples of pure-jump strict local martingales," Papers 1405.2669, arXiv.org, revised Jun 2015.
    8. Gonon, Lukas & Teichmann, Josef, 2020. "Linearized filtering of affine processes using stochastic Riccati equations," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 394-430.
    9. Mayerhofer, Eberhard, 2012. "Affine processes on positive semidefinite d×d matrices have jumps of finite variation in dimension d>1," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3445-3459.

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