Completely asymmetric Lévy processes confined in a finite interval

By Amaury Lambert. 2000

70 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/b28c13090f51ca3aa6d7de6fb3f76a7da3c5a7a4

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Citations in the corpus

Fluctuations of Lévy Processes with Applications (2014, methodology): “Nonetheless, Lambert (2002) gives a path-wise construction with the help of excursion theory and Itô synthesis; a technique which goes beyond the scope of this text.”
Smoothness of scale functions for spectrally negative Lévy processes (2009, unknown): “In [13] it is shown that the latter is the case if for example the process X has paths of unbounded variation (and in particular if it possesses a Gaussian component) or if X has paths of bounded variation and the Lévy measure is absolutely continuous with respect to Lebesgue measure.”
Evaluating Scale Functions of Spectrally Negative Lévy Processes (2008, background): “For a literature review, we refer the reader to [2], [5], [6], [18], [22], and the literature therein.”
Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “Smoothness The following facts are taken from Lambert (2000), Chan and Kyprianou (2007), Kyprianou et al. (2008) and Doney (2005b).”
On the optimal dividend problem for a spectrally negative Lévy process (2007, background): “On (0,∞) the function y 7→ W (q)(y) is right- and left-differentiable and, as shown in [18], under the condition (3.”
Exit problems for spectrally negative Levy processes and applications to (Canadized) Russian options (2004, background): “Furthermore, if X has unbounded variation or if X has bounded variation and satisfies (AC), the restricted function W v |(0,∞) is continuously differentiable (see [16] and [4]).”
Refracted Lévy processes (2008, unknown): “See, for example, [23] and [22].”
Quasi-stationary Distributions : A Bibliography (2000, background): “Cattiaux, Collet, Lambert, Mart́ınez, Méléard and San Mart́ın [70] Collet, Mart́ınez and San Mart́ın [86] Kennedy [197] Kao [189] Lambert [242] Pinsky [330] Pinsky [331] Jacka and Roberts [184] Jacka and Roberts [186] Kyprianou and Palmowski [236] Lambert [244] Lladser and San Mart́ın [264] Steinsal”
Multifractal spectra and precise rates of decay in homogeneous fragmentations (2006, unknown): “Throughout this work we will make the following assumption, which is easily seen to imply (6) (in fact we can even show that the two are equivalent): In the next subsection, we will give some results about L´evy processes that will be needed in the sequel, and apply for Y t = vt − ξ ( t ).”
Special, conjugate and complete scale functions for spectrally negative Lévy processes (2007, background): “The real value of scale functions as a class with which one may express a whole range of fluctuation identities for spectrally negative Lévy processes became apparent in the work of [12; 13] and [6; 7] and an ensemble of subsequent articles; see for example [42], [2], [46; 47; 48; 49], [39], [20] an”
Distributional Study of De Finetti's Dividend Problem for a General Lévy Insurance Risk Process (2007, background): “To complete the proof recall from Lambert (2000) that n(s > a) = Wf(a)/W(a) and from Avram et al (2004) that W(q)(x) = ^(q)xW^(q)(x).”
On Exit and Ergodicity of the Spectrally One-Sided Lévy Process Reflected at Its Infimum (2004, background): “Important elements in the proof of the ergodic properties and the exponential decay are the special form of the earlier computed resolvent measure together with special properties of fluctuation theory of completely asymmetric Lévy processes, elementary properties of analytic functions and the…”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, unknown): “Otherwise, when X has paths of bounded variation, a necessary and sufficient condition for W (q) to be continuous is that the jump measure Π has no atoms (cf. Lambert, 2000; Kyprianou, Rivero and Song, 2008b).”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, methodology): “See Caballero et al. [26] and Kyprianou and Pardo [67] for further computations in this spirit and Lambert [73] for further applications in population biology.”