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Brownian Semistationary Processes And Conditional Full Support

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  • MIKKO S. PAKKANEN

    (Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014 Helsingin yliopisto, Finland)

Abstract

In this note, we study the infinite-dimensional conditional laws of Brownian semistationary processes. Motivated by the fact that these processes are typically not semimartingales, we present sufficient conditions ensuring that a Brownian semistationary process has conditional full support, a distributional property that has two important implications. It ensures, firstly, that the process admits no free lunches under proportional transaction costs, and secondly, that it can be approximated pathwise (in the sup norm) by semimartingales that admit equivalent martingale measures.

Suggested Citation

  • Mikko S. Pakkanen, 2011. "Brownian Semistationary Processes And Conditional Full Support," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 579-586.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:04:n:s0219024911006747
    DOI: 10.1142/S0219024911006747
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    References listed on IDEAS

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    1. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Modelling energy spot prices by Lévy semistationary processes," CREATES Research Papers 2010-18, Department of Economics and Business Economics, Aarhus University.
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    Cited by:

    1. Bennedsen, Mikkel, 2017. "A rough multi-factor model of electricity spot prices," Energy Economics, Elsevier, vol. 63(C), pages 301-313.
    2. Christoph Czichowsky & Walter Schachermayer, 2015. "Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion," Papers 1505.02416, arXiv.org, revised Aug 2016.
    3. Takaki Hayashi & Yuta Koike, 2017. "No arbitrage and lead-lag relationships," Papers 1712.09854, arXiv.org.
    4. Mikkel Bennedsen, 2015. "Rough electricity: a new fractal multi-factor model of electricity spot prices," CREATES Research Papers 2015-42, Department of Economics and Business Economics, Aarhus University.
    5. Christian Bender & Mikko S. Pakkanen & Hasanjan Sayit, 2013. "Sticky continuous processes have consistent price systems," CREATES Research Papers 2013-38, Department of Economics and Business Economics, Aarhus University.
    6. Li, Yuan & Pakkanen, Mikko S. & Veraart, Almut E.D., 2023. "Limit theorems for the realised semicovariances of multivariate Brownian semistationary processes," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 202-231.
    7. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, arXiv.org.
    8. Mikkel Bennedsen, 2016. "Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data," Papers 1608.01895, arXiv.org, revised Mar 2018.
    9. Pakkanen, Mikko S. & Sottinen, Tommi & Yazigi, Adil, 2017. "On the conditional small ball property of multivariate Lévy-driven moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 749-782.
    10. Christian Bender & Mikko S. Pakkanen & Hasanjan Sayit, 2013. "Sticky continuous processes have consistent price systems," Papers 1310.7857, arXiv.org, revised Aug 2014.
    11. Mikkel Bennedsen, 2016. "Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data," CREATES Research Papers 2016-21, Department of Economics and Business Economics, Aarhus University.

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