On Exit and Ergodicity of the Spectrally One-Sided Lévy Process Reflected at Its Infimum

By Martijn Pistorius. 2004

153 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/2544e18955b6e140b02d30ba3ad3c44c21567572

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Citations in the corpus

Optimal dividends problem with a terminal value for spectrally positive Levy processes (2013, methodology): “…Lévy process with initial value b−x. Define T̃b = inf{t > 0 : Yb(t) ≥ b}, then E [ e−qTb |Ub(0) = x ] = E [ e−qT̃b |Yb(0) = b− x ] = Z(q)(b− x) Z(q)(b) , where in the last step we have used the result of Proposition 2 (i) in Pistorius (2004), see also Theorem 2.8 (i) in Kuznetsov et al (2012).”
De Finetti's optimal dividends problem with an affine penalty function at ruin (2010, unknown): “0 ePx ( U b t ∈ dy, t < σ ) dt = W (q)(x) W (q)′(b) W (b− dy)−W (x− y) dy (see Theorem 1 (ii) in [28]), we deduce (14).”
Occupation densities in solving exit problems for Markov additive processes and their reflections (2011, methodology): “For Lévy processes this technique complements the use of martingales (see [29, 32, 6]), potential densities (see [36]), and excursion calculations (see [18, 35]).”
Evaluating Scale Functions of Spectrally Negative Lévy Processes (2008, methodology): “But, nonetheless, it exhibits the important properties of the scale function, as specified in Proposition 1 and those found in, among others, [7], [15], [17], and [21].”
On the drawdown of completely asymmetric Lévy processes (2011, background): “[31] M.R. Pistorius (2007), An Excursion-Theoretical Approach to Some Boundary Crossing Problems and the Skorokhod Embedding for Reflected Lévy Processes.”
On Gerber–Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function (2011, background): “1) and Pistorius [34], Theorem 1 (see also proof of Proposition 5.”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, background): “Pistorius [87, 86] also shows that a similar agenda to the above can be carried out with regard to reflected spectrally negative Lévy processes.”
General tax Structures and the Lévy Insurance Risk Model (2009, background): “[18] for example) that excursions begin with a jump and the entrance law is given by d−1ν(dx).”
Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “The left hand side of (49) is the Laplace transform of W (x), and we know it is an analytic function for R(θ) > Φ(q).”
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”
On magnitude, asymptotics and duration of drawdowns for L\'{e}vy models (2015, background): “Moreover, by a similar approximation argument, one can solve for the joint distribution of equation (3.6) but with the law of Yτa , which then recovers the sextuple law in Theorem 1 of Mijatović and Pistorius [29] (the running minimum at τa can also be easily incorporated).”