Well-balanced Lévy driven Ornstein–Uhlenbeck processes
Copyright policy )Well-balanced Lévy driven Ornstein–Uhlenbeck processes
Abstract In this paper we introduce the well-balanced Lévy driven Ornstein–Uhlenbeck process as a moving average process of the form X t = ∫ exp(-λ|t-u|)dL u . 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.
- TU Dortmund University Germany
Lèvy process, 330, 60G10, 60E07, 91B24, autocorrelation, Infinitely divisible distributions; stable distributions, semimartingale, 610, 310, financial modelling, Characteristic functions; other transforms, in finitely divisible distribution, FOS: Mathematics, info:eu-repo/classification/ddc/310, info:eu-repo/classification/ddc/610, Infinitely divisible distribution, info:eu-repo/classification/ddc/330, Lévy process, Probability (math.PR), infinitely divisible distribution, 620, Autocorrelation, Semimartingal, Financial modelling, Ornstein-Uhlenbeck process, info:eu-repo/classification/ddc/620, Financial applications of other theories, Mathematics - Probability
Lèvy process, 330, 60G10, 60E07, 91B24, autocorrelation, Infinitely divisible distributions; stable distributions, semimartingale, 610, 310, financial modelling, Characteristic functions; other transforms, in finitely divisible distribution, FOS: Mathematics, info:eu-repo/classification/ddc/310, info:eu-repo/classification/ddc/610, Infinitely divisible distribution, info:eu-repo/classification/ddc/330, Lévy process, Probability (math.PR), infinitely divisible distribution, 620, Autocorrelation, Semimartingal, Financial modelling, Ornstein-Uhlenbeck process, info:eu-repo/classification/ddc/620, Financial applications of other theories, Mathematics - Probability
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