Well-balanced Lévy driven Ornstein–Uhlenbeck processes

Schnurr Alexander and Woerner Jeannette H. C.
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Schnurr Alexander: Technische Universität Dortmund, Fakultät für Mathematik, LS IV, Dortmund, Deutschland

Statistics & Risk Modeling, 2011, vol. 28, issue 4, 343-357

Abstract: 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.

Keywords: Semimartingale; Ornstein-Uhlenbeck process; Lévy process; infinitely divisible distribution; autocorrelation (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:28:y:2011:i:4:p:343-357:n:4

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DOI: 10.1524/strm.2011.1089

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