Well-balanced Lévy driven Ornstein–Uhlenbeck processes

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.