Infinite divisibility of the hyperbolic and generalized inverse Gaussian distributions

By Ole E. Barndorff-Nielsen, C. Halgreen. 1977

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Citations in the corpus

Characteristic Kernels and Infinitely Divisible Distributions (2014, background): “The final example considers the GH distribution (Barndorff-Nielsen and Halgreen, 1977).”
Stationary-increment Student and variance-gamma processes (2006, unknown): “Here X t | V = N (µ + θV, σ 2 V ) , where V has an inverse gamma distribution as above (and, thus, 1 / not with unit expectation). t form f GIG (x) = α/ hyperbolic (GH) distribution (see Barndorff-Nielsen (1977)) with PDF (cid”
On the stick-breaking representation of normalized inverse Gaussian priors (2012, background): “Given that generalized inverse Gaussian random variables are infinitely divisible [2], the normalized generalized inverse Gaussian distribution represents another example of the class of normalized infinitely divisible distributions studied in [7].”
Semi-parametric modelling in finance: theoretical foundations (2002, background): “It was shown by Barndorff-Nielsen and Halgreen (1977) that GIG is infinitely divisible, and by Halgreen (1979) that GIG is self-decomposable.”
Hyperbolic Processes in Finance (2003, background): “Barndor-Nielsen & Halgreen (1977) showed that generalized inverse Gaussian distributions are innitely divisible.”
Generalized Hyperbolic and Inverse Gaussian Distributions: Limiting Cases and Approximation of Processes (2003, methodology): “11) Barndorff-Nielsen and Halgreen [6] have shown that GH and GIG distributions are infinitely divisible; we get this by a different method in section 5 and give explicit Lévy-Khintchine representations.”
Modelling energy spot prices by volatility modulated Levy-driven Volterra processes (2013, background): “That, in fact, is the case since the GIG laws are self-decomposable, cf. Halgreen [48] and Jurek and Vervaat [51].”
Optimal stopping and perpetual options for Lévy processes (2002, methodology): “The evolution of B is deterministic, with Bt = e, r ≥ 0, (where B0 = 1 for simplicity), and the stock is random, and evolves according to the formula St = S0e , S0 > 0, (1) where X = {Xt}t≥0 is a Lévy process.”
Pure jump L'evy processes for asset price modeling (2002, unknown): “Barndorff-Nielsen and Halgreen (1977) show that the hyperbolic distribution can be represented as a mixture of normals, where the mixing distribution is a generalized inverse Gaussian with density ( ) ( )ωγ γ ω 12K xh = exp ( ) +− − xx ωγ 1 2 1 for x > 0 13 Let 2δγ = and 22 βαω −= and…”