Introductory Lectures on Fluctuations of Lévy Processes with Applications

By Andreas E. Kyprianou. 2006

1,053 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4da3bf95e911a672f9653f13e87b46d39a9ad2fd

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Citations in the corpus

A Lévy Insurance Risk Process with Tax (2008, background): “Under P (q) u , X is still a spectrally negative Lévy process, but now with W (q) as its 0-scale function, which are given by e W (q)(x) = W(x); in addition, under this measure, X drifts to +∞ (see Chapter 8 of [14] for details).”
Smoothness of scale functions for spectrally negative Lévy processes (2009, neutral): “5 in [10]).”
Some properties of Prabhakar-type fractional calculus operators (2015, positive): “Let us thus consider an α -stable subordinator Vα(t) , t 0, that is an increasing spectrally positive Lévy process such that Eexp(−λVα(t)) = exp(−tλ α) [19, 4].”
Boundary Harnack principle for subordinate Brownian motions (2007, background): “10 of [19] that the process X does not creep upwards.”
Parisian ruin probability for spectrally negative Lévy processes (2011, methodology): “For background on spectrally negative Lévy processes we referer to Section 8 of Kyprianou [7].”
Optimal dividends problem with a terminal value for spectrally positive Levy processes (2013, positive): “For more details on spectrally positive Lévy processes, the reader is referred to Bertoin (1996), Sato (1999) and Kyprianou (2006).”
Valuing equity-linked death benefits and other contingent options: A discounted density approach (2012, background): “(2.35) For more general results, see Section XI.4d of Asmussen and Albrecher (2010) and Chapter 6 of Kyprianou (2006).”
On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes (2008, neutral): “We refer to [22], Chapter 8, for more information on scale functions.”
Novel scaling limits for critical inhomogeneous random graphs (2009, neutral): “, [6, 29] for more information on Lévy processes), with exponent ψ(θ) [for which E(e−θ(Rt−R0)) = e−tψ(θ)] given by ψ(θ) = (c − ab)θ + ∞ ∑ i=2 ai−α[1 − e−θbi − bθi−α].”
An optimal dividends problem with transaction costs for spectrally negative Lévy processes (2009, positive): “When the Lévy measure has a density which is log-convex, Kyprianou et al. [18] proved that W (q) is strictly increasing and strictly convex on (a (q) (x) for all x ≥ 0 which is necessarily finite since lim x→∞ W (q) (x) = ∞.”
Proof(s) of the Lamperti representation of Continuous-State Branching Processes (2008, methodology): “To explain the heuristics behind the Lamperti transformation (implicit in [20, 26] and also found in [3, 19]), let us note that for any state i 6∈ {0,∞}, the size of the jump of Z starting from i does not depend on i.”
Occupation times of intervals until first passage times for spectrally negative Lévy processes (2012, background): “Most results are taken, or can easily be derived, from [6].”