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Diffusion-based models for financial markets without martingale measures

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  • Claudio Fontana
  • Wolfgang J. Runggaldier

Abstract

We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and portfolio optimisation problems can be meaningfully solved. Relying partly on the recent literature, we provide necessary and sufficient conditions for market viability in terms of the market price of risk process and martingale deflators. Regardless of the existence of a martingale measure, we show that the financial market may still be complete and contingent claims can be valued under the original (real-world) probability measure, provided we use as numeraire the Growth-Optimal Portfolio.

Suggested Citation

  • Claudio Fontana & Wolfgang J. Runggaldier, 2012. "Diffusion-based models for financial markets without martingale measures," Papers 1209.4449, arXiv.org, revised Feb 2013.
  • Handle: RePEc:arx:papers:1209.4449
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    References listed on IDEAS

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    9. Hardy Hulley & Martin Schweizer, 2010. "M6 - On Minimal Market Models and Minimal Martingale Measures," Research Paper Series 280, Quantitative Finance Research Centre, University of Technology, Sydney.
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    14. 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. Jacopo Mancin & Wolfgang J. Runggaldier, 2015. "On the Existence of Martingale Measures in Jump Diffusion Market Models," Papers 1511.08349, arXiv.org.
    2. Xavier Warin, 2016. "The Asset Liability Management problem of a nuclear operator : a numerical stochastic optimization approach," Papers 1611.04877, arXiv.org.
    3. Fontana, Claudio & Grbac, Zorana & Jeanblanc, Monique & Li, Qinghua, 2014. "Information, no-arbitrage and completeness for asset price models with a change point," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3009-3030.

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