Special, conjugate and complete scale functions for spectrally negative Lévy processes

By Andreas E. Kyprianou, V. Rivero. 2007

64 citations recorded by the source corpus.

Following from recent developments in Hubalek and Kyprianou [28], the objective of this paper is to provide further methods for constructing new families of scale functions for spectrally negative Levy processes which are completely explicit. This is the result of an observation in the aforementioned paper which permits feeding the theory of Bernstein functions directly into the Wiener-Hopf factorization for spectrally negative Levy processes. Many new, concrete examples of scale functions are offered although the methodology in principle delivers still more explicit examples than those listed.

Subfields: Finance, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/4273fe486c759951260cea7f6f24cc3da45d6d9b

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Citations in the corpus

General tax Structures and the Lévy Insurance Risk Model (2009, unknown): “…−κ); SU τ−0 ∈ dθ, Uτ−0 − ∈ dy, −Uτ−0 ∈ dz) = 1 1 − γ (γ̄−1(θ)) exp { − ∫ θ x W(α)′(v) W(α)(v)(1 − γ (γ̄−1(v))) dv } × [{ W(β)′(θ − y)− W (β)′(θ) W(β)(θ) W(β)(θ − y) } ν(y + dz)1{y<θ} dy +W(β)(0+)ν(θ + dz)δθ (dy) ] dθ, where δθ (dy) is the Dirac measure which assigns unit mass to the point θ .”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, background): “In [73] the interested reader may find a discussion about the conjugated pairs arising in this construction.”
An optimal dividends problem with transaction costs for spectrally negative Lévy processes (2009, unknown): “We refer to the papers [12, 17, 18] for an updated account on explicit examples of scale functions and their properties.”
An Insurance Risk Model with Parisian Implementation Delays (2013, unknown): “As will be shown, all our results are expressed in terms of scale functions for which many explicit examples are known; see, e.g., Hubalek and Kyprianou (2010), Kyprianou and Rivero (2008).”
An Optimal Dividends Problem with a Terminal Value for Spectrally Negative Lévy Processes with a Completely Monotone Jump Density (2009, unknown): “We refer the reader to the papers [13], [17], and [19] for an updated account on explicit examples of scale functions and their properties.”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, unknown): “Hubalek and Kyprianou (2008); Kyprianou and Rivero (2008); Kyprianou and Patie (2008) contain many more examples as well as methodologies for generating a plethora of other explicit examples; that is to say, examples for which the scale function and the characteristic triplet of the underlying Lévy…”
Convexity and Smoothness of Scale Functions and de Finetti’s Control Problem (2008, background): “4 are weaker than those in Corollary 2 in [23], because every Bernstein function f is a non-decreasing concave function, and f ′ and −f ′′ are completely monotone functions with limx↓0 xf ′(x) = 0.”
Smoothness of scale functions for spectrally negative Lévy processes (2009, unknown): “and hence the sum with respect to n of the second term on the right hand side of (17), is uniformly and absolutely convergent on (2ǫ, a).”