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Well-balanced Lévy driven Ornstein–Uhlenbeck processes


  • Schnurr Alexander

    (Technische Universität Dortmund, Fakultät für Mathematik, LS IV, Dortmund, Deutschland)

  • Woerner Jeannette H. C.


In this paper we introduce the well-balanced Lévy driven Ornstein–Uhlenbeck process as a moving average process of the form Xt = ∫ exp(-λ|t-u|)dLu. In contrast to Lévy driven Ornstein–Uhlenbeck processes the well-balanced form possesses continuous sample paths and an autocorrelation function which is decreasing not purely exponential but of the order λ|u|exp(-λ|u|). Furthermore, depending on the size of λ it allows both for positive and negative correlation of increments. We indicate how the well-balanced Ornstein–Uhlenbeck process might be used as mean or volatility process in semimartingale models.

Suggested Citation

  • Schnurr Alexander & Woerner Jeannette H. C., 2011. "Well-balanced Lévy driven Ornstein–Uhlenbeck processes," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 343-357, December.
  • Handle: RePEc:bpj:strimo:v:28:y:2011:i:4:p:343-357:n:4

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    References listed on IDEAS

    1. Claudia Kluppelberg & Thilo Meyer-Brandis & Andrea Schmidt, 2010. "Electricity spot price modelling with a view towards extreme spike risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 963-974.
    2. Cardinali Alessandro & Nason Guy P, 2011. "Costationarity of Locally Stationary Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-35, January.
    3. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Modelling electricity forward markets by ambit fields," CREATES Research Papers 2010-41, Department of Economics and Business Economics, Aarhus University.
    4. 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.
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