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OLD AND NEW EXAMPLES OF SCALE FUNCTIONS FOR SPECTRALLY Negative Lévy Processes
, 2009
"... We give a review of the state of the art with regard to the theory of scale functions for spectrally negative Lévy processes. From this we introduce a general method for generating new families of scale functions. Using this method we introduce a new family of scale functions belonging to the Gaussi ..."
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Cited by 49 (13 self)
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We give a review of the state of the art with regard to the theory of scale functions for spectrally negative Lévy processes. From this we introduce a general method for generating new families of scale functions. Using this method we introduce a new family of scale functions belonging to the Gaussian Tempered Stable Convolution (GTSC) class. We give particular emphasis to special cases as well as crossreferencing their analytical behaviour against known general considerations.
On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes
, 2007
"... We consider the classical optimal dividend control problem which was proposed by de Finetti [Trans. XVth Internat. Congress Actuaries ..."
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Cited by 41 (5 self)
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We consider the classical optimal dividend control problem which was proposed by de Finetti [Trans. XVth Internat. Congress Actuaries
Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels, Finance and Stochastics
"... endogenous bankruptcy levels ..."
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A note on scale functions and the time value of ruin for Lévy insurance risk processes
, 2009
"... We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important con ..."
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Cited by 22 (3 self)
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We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important contributions of Zhou (2005) we provide an explicit characterization of a generalized version of the GerberShiu function in terms of scale functions, streamlining and extending results available in the literature.
Convexity and smoothness of scale functions and de Finetti’s control problem
, 2008
"... Motivated by a classical control problem from actuarial mathematics, we study smoothness and convexity properties of qscale functions for spectrally negative Lévy processes. Continuing from the very recent work of [2] and [24] we strengthen their collective conclusions by showing, amongst other res ..."
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Cited by 16 (6 self)
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Motivated by a classical control problem from actuarial mathematics, we study smoothness and convexity properties of qscale functions for spectrally negative Lévy processes. Continuing from the very recent work of [2] and [24] we strengthen their collective conclusions by showing, amongst other results, that whenever the Lévy measure has a nonincreasing density which is log convex then for q> 0 the scale function W (q) is convex on some half line (a ∗ , ∞) where a ∗ is the largest value at which W (q)′ attains its global minimum. As a consequence we deduce that de Finetti’s classical actuarial control problem is solved by a barrier strategy where the barrier is positioned at height a ∗.
De Finetti’s optimal dividends problem with an affine penalty function at ruin
 Insurance Math. Econom
"... Abstract. In a Lévy insurance risk model, under the assumption that the tail of the Lévy measure is logconvex, we show that either a horizontal barrier strategy or the takethemoneyandrun strategy maximizes, among all admissible strategies, the dividend payments subject to an affine penalty func ..."
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Cited by 15 (3 self)
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Abstract. In a Lévy insurance risk model, under the assumption that the tail of the Lévy measure is logconvex, we show that either a horizontal barrier strategy or the takethemoneyandrun strategy maximizes, among all admissible strategies, the dividend payments subject to an affine penalty function at ruin. As a key step for the proof, we prove that, under the aforementioned condition on the jump measure, the scale function of the spectrally negative Lévy process has a logconvex derivative. 1. Introduction and
Occupation times of spectrally negative Lévy processes with applications. Stochastic Process
 Appl
, 2011
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An optimal dividends problem with a terminal value for spectrally negative Lévy processes with a . . .
, 2008
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Phasetype fitting of scale functions for spectrally negative Lévy processes
, 2013
"... We study the scale function of the spectrally negative phasetype Lévy process. Its scale function admits an analytical expression and so do a number of its fluctuation identities. Motivated by the fact that the class of phasetype distributions is dense in the class of all positivevalued distrib ..."
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Cited by 12 (10 self)
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We study the scale function of the spectrally negative phasetype Lévy process. Its scale function admits an analytical expression and so do a number of its fluctuation identities. Motivated by the fact that the class of phasetype distributions is dense in the class of all positivevalued distributions, we propose a new approach to approximating the scale function and the associated fluctuation identities for a general spectrally negative Lévy process. Numerical examples are provided to illustrate the effectiveness of the approximation method.
On scale functions of spectrally negative Lévy processes with phasetype jumps
, 2010
"... We study the scale function for the class of spectrally negative Lévy processes with phasetype jumps. We consider both the compound Poisson case and the unbounded variation case with diffusion components, and obtain the corresponding scale functions explicitly. Motivated by the fact that the clas ..."
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Cited by 11 (5 self)
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We study the scale function for the class of spectrally negative Lévy processes with phasetype jumps. We consider both the compound Poisson case and the unbounded variation case with diffusion components, and obtain the corresponding scale functions explicitly. Motivated by the fact that the class of phasetype distributions is dense in the class of all positivevalued distributions, we propose a new approach to approximating the scale function for a general spectrally negative Lévy process. We illustrate, in numerical examples, its effectiveness by obtaining the scale functions for Lévy processes with longtail distributed jumps.