WIENER-HOPF FACTORIZATION FOR LEVY PROCESSES HAVING POSITIVE JUMPS WITH RATIONAL TRANSFORMS

By Alan L. Lewis, Ernesto Mordecki. 2008

104 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/9b06fc2e179baae40d11b16dd956d15f07f04b34

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Citations in the corpus

Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes (2010, background): “There also exist several integral representation for φq in terms of P(Xt ∈ dx) (see [5], [17] or [13]) or in terms of Ψ(z) ([4], [15]).”
Some explicit identities associated with positive self-similar Markov processes. (2007, unknown): “self-similar Markov processes.”
On extrema of stable processes. (2010, methodology): “We start with the following general integral representation for φq (z), which was first derived in [22] (Lemma 4.”
Fluctuations of Lévy Processes with Applications (2014, methodology): “See for example the up-to-date account in Nelson (2006). Inspired by this methodology, a limited volume of recent literature has proposed to address the modelling of multi-dimensional Lévy processes by working with copulas on the Lévy measure.”
Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “The results are implicitly contained in Mordecki and Lewis (2005) and Kou and Wang (2003) and we exclude the calculations here.”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, methodology): “[8] and Pistorius [84], while Wiener–Hopf factorization for a more general class of processes having positive jumps of rational transform was obtained by Lewis and Mordecki [74].”
VALUATION OF CONTINUOUSLY MONITORED DOUBLE BARRIER OPTIONS AND RELATED SECURITIES (2009, unknown): “If the singularity of the integrand is removable, then one can shift the line of integration to the real line and obtain (2.13) with ω± = 0—see Lewis and Mordecki (2008).”
Conditioned stable Levy processes and Lamperti representation. (2006, methodology): “The law of the overall minimum ξ ↑ of ξ ↑ is given by: This computation is closely related to risk theory and in particular proposition 2 provides an explicit form of the ruin probability at level z ≥ 0, i.e. for this class of L´evy processes, see the recent paper by Lewis and Mordecki [11].”