A Potential-theoretical Review of some Exit Problems of Spectrally Negative Lévy Processes

By Martijn Pistorius. 2005

56 citations recorded by the source corpus.

Subfields: Applied Mathematics, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fc30e1163574aa1f56e4a7a8f79e2e0f56c641f6

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In Applied Mathematics

In Management Science and Operations Research

In Mathematical Physics

Citations in the corpus

The McKean stochastic game driven by a spectrally negative Lévy process (2008, methodology): “Combining these facts, (25), (26) and using Lemma 11 we find”
An Excursion-Theoretical Approach to Some Boundary Crossing Problems and the Skorokhod Embedding for Reflected Lévy Processes (2007, unknown): “[20] for a proof.”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, unknown): “It is known from the general phenomenon of creeping of Lévy processes that Xτ− = Xτ− = 0 on {Xτ = 0} and this occurs with probability Ex(e−qτ ;Xτ = 0) = σ2 2 { W (q)′(x)− Φ(q)W (q)(x) } (cf. Pistorius, 2005).”
Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “…became apparent in the work of Chaumont (1994, 1996) of Bertoin (1996, 1997) and an ensemble of subsequent articles; see for example Lambert (2000), Avram et al. (2004), Pistorius (2003, 2004, 2005, 2007), Kyprianou and Palmowski (2006), Doney and Kyprianou (2006) and Doney (1991, 2005a, 2007).”
Refracted Lévy processes (2008, methodology): “Since U is the sum of a continuous process and a Lévy process, it is quasi-left continuous and hence we can use Proposition 1(i) in [25] to deduce”
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”
Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory (2011, background): “The fluctuation theory for spectrally negative Lévy processes has been the object of several studies over the last 40 years, among many others, see Emery (1973), Bingham (1975) and Bertoin (1997); We refer to Kyprianou and Palmowaki (2005) and Pistorius (2005) for exhaustive reviews.”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, result): “Many of the results in this section are taken from the recent work [15, 84, 9, 83].”