Lévy-Driven Carma Processes

By Peter J. Brockwell. 2001

104 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/47aff140343fb03c82b3be1d3cd21a4f8fe08d56

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Citations in the corpus

Generalised Ornstein-Uhlenbeck Processes and the Convergence of Levy Integrals (2005, background): “As mentioned, subordinated perpetuities occur in various applications, especially in Finance (e.g., [3], [9], [40], [41]) and in time series modelling (e.g., Brockwell [ 6 ], [7]).”
Non-Gaussian OU based models and some of their uses in financial economics (2000, methodology): “Given f(·) such a process is stationary and This type of model has been used in storage theory by, for example, Cinlar and Pinsky (1972), Harrison and Resnick (1976) and Brockwell, Resnick, and Tweedie (1982). Extensions to the ARMA case are discussed by Brockwell (2001).”
Estimation for Non-Negative Lévy-Driven CARMA Processes (2011, methodology): “If L is a second-order subordinator and p > q, the L-driven CARMA(p,q) with parameters {a1, . . . ,ap;b1, . . . ,bq} is defined (see Brockwell 2001) via the state-space representation of the formal stochastic differential equation a(D)Y(t) = b(D)DL(t), (2.1) where D denotes differentiation with…”
Estimation of continuous-time stochastic volatility models with jumps using high-frequency data (2009, methodology): “This model was analyzed in Brockwell (2001a) and Todorov and Tauchen (2006) among others.”
Lévy-driven and fractionally integrated ARMA processes with continuous time parameter (2005, background): “…ofL(t), we nd that the cumulant generating function of Y (t) is(2:17) logE(exp(i Y (t))) = Z 10 ( g(u))du:More generally it can be shown (see Brockwell (2001)) that the cumulant generatingfunction of Y (t1); Y (t2); : : : ; Y (tn), (t1 < t2 < < tn) is(2:18) logE[exp(i 1Y (t1) + + i nY…”
Futures pricing in electricity markets based on stable CARMA spot models (2012, background): “These processes incorporate in an eﬃcient way memory eﬀects and mean-reversion, and generalise Ornstein-Uhlenbeck processes in a natural way (see Brockwell [11]).”
A multivariate Ornstein-Uhlenbeck type stochastic volatility model (2009, methodology): “To obtain such a flexible behavior in the univariate case extensions such as the class of CARMA models, proposed by Brockwell (2001) with appropriate positivity restrictions can be applied, see e.g. Todorov and Tauchen (2006).”