A note on scale functions and the time value of ruin for Levy insurance risk processes

By Enrico Biffis, Andreas E. Kyprianou. 2010

98 citations recorded by the source corpus.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/500e1f7f3116068f36505e9f0e951ceccc9c3c8c

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Citations in the corpus

The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, background): “[19, 20]) which even goes a little further than what classical Gerber–Shiu theory demands in that it also incorporates distributional information on the infimum of the surplus prior to ruin.”
On Gerber–Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function (2011, background): “Given results concerning the smoothness of scale functions (see, e.g., Kyprianou et al. [24]), it is not to be expected that the candidate value-function is a classical solution of the HJB equation.”
Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory (2011, methodology): “…mathematics, the first passage problem is very important to the ruin problems; see, for example, among others, Yang and Zhang (2001), Klüppelberg et al. (2004), Huzak et al. (2004a, 2004b), Zhou (2005), Garrido and Morales (2006), Biffis and Kyprianou (2010) and Billis and Morales (2010).”
De Finetti's optimal dividends problem with an affine penalty function at ruin (2010, unknown): “As the Lévy process X has no positive jumps, its Laplace transform exists and is given by E [ eθXt ] = etψ(θ), for θ ≥ 0 and t ≥ 0, where ψ(θ) = γθ + 1 2 σ2θ2 − ∫ ∞ 0 ( 1− e−θz − θzI(0,1](z) ) ν(dz), for γ ∈ R and σ ≥ 0, and where ν is a measure on (0,∞) such that∫ ∞ 0 (1 ∧ z2) ν(dz) ∞.”