Lévy processes and infinitely divisible distributions
Citations
6 citations
6 citations
Cites background or methods from "Lévy processes and infinitely divis..."
..., one can use the contour deformation Lω;χ+α for α ∈ [1, 4), rather than α ∈ [1, 2), with the understanding that, for α ∈ [2, 4), the contour belongs to an appropriate Riemann surface....
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...PARABOLIC IFT METHOD (CASE x′ ≥ 0, ω > 0) 153 • if x′ > 0 and ν ∈ [0, 1), then α0 = min{3, 1 + 1/ν}; • if x′ = 0 and ν ∈ [0, 1), then α0 = min{4, 1 + 1/ν}; • if x′ ≥ 0 and ν ∈ [1, 2], then α0 = 1 + 1/ν....
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...As for the put option, one can use the contour transformation ξ 7→ χα (ξ) for the wider range α ∈ [1, 4), with the understanding that, for α ∈ [2, 4), the contour belongs to the appropriate Riemann surface....
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...For an exposition of the general theory of Lévy processes and their applications to pricing derivative securities, we refer the reader to [7, 77, 2] and [18, 32, 82], respectively....
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...For α ∈ [1, 2], one considers the conformal map χα , defined on the half-plane Im ξ > λ− by χα (ξ) = iλ− + i(−λ− − 1)(−λ− − iξ)....
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6 citations
Cites background from "Lévy processes and infinitely divis..."
...6 in [41] und nach doppelter Anwendung der Cauchy-SchwarzUngleichung....
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...Wir orientieren uns weitestgehend an [29], was einer direkten Fortsetzung der univariaten Idee in [41] entspricht und vereinbaren folgende Sprechweisen, wobei wir auf die zum Teil übliche Bedingung der stochastischen Stetigkeit (oder der Stetigkeit in Verteilung) zunächst verzichten....
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...6 in [41]) und der Cauchy-Schwarz-Ungleichung unmittelbar, dass | cos〈f(s)tn, x〉 − 1| ≤ 2 min{1, ‖f(s)‖(2)‖tn‖(2)‖x‖(2)} ≤ C(s) min{1, ‖x‖(2)}, n ∈ N, wobei C(s) := 2 max{1, ‖f(s)‖2K2}....
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...Ähnlich umfangreiche Darstellungen findet man diesbezüglich beispielsweise auch in [41]....
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6 citations
Cites background or methods from "Lévy processes and infinitely divis..."
...(10) Of course, a rv X with chf η(u) is also said to be sd when its law is sd, and looking at the definitions this means that for every 0 a 1 we can always find two independent rv ’s – a Y with the same law of X, and a Za with chf χa(u) – such that in distribution X d = aY + Za (11) Hereafter the rv Za will be called the a-remainder of X and in general has an id (see Sato [45])....
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...We recall that a law with chf η(u) is said to be sd (see Sato [45] or Cufaro Petroni [13]) when for every 0 < a < 1 we can find another law with chf χa(u) such that η(u) = η(au)χa(u)....
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...Hereafter the rv Za will be called the a-remainder of X and in general has an id (see Sato [45])....
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...We recall that a law with chf η(u) is said to be sd (see Sato [45] or Cufaro Petroni [13]) when for every 0 a 1 we can find another law with chf χa(u) such that η(u) = η(au)χa(u)....
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6 citations
Cites background from "Lévy processes and infinitely divis..."
...The comprehensive study of this class is given in brilliant books by Samorodnitsky and Taqqu (1994), Bertoin (1998), Sato (1999)....
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References
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