A Martingale Review of some Fluctuation Theory for Spectrally Negative Lévy Processes

By Andreas E. Kyprianou, Zbigniew Palmowski. 2005

63 citations recorded by the source corpus.

Subfields: Management Information Systems, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bad5f0f521eaa11d84599f8cbaf975b622caceb7

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Citations in the corpus

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]).”
Ruin Probability with Parisian Delay for a Spectrally Negative Lévy Risk Process (2010, unknown): “Moreover, from [18] we know that E e (β)Xeω = ω( (β)− (ω)) (ω)(β − ω) and that P(−Xeω ∈ dz) = ω (ω) W(ω)(dz)− ωW(z) dz.”
Fluctuations of spectrally negative Markov additive processes (2008, methodology): “We may thus use the conclusions of the previous paragraph in (17) to deduce Ex ( e−qτ + a 1(τ+ a <τ− 0 ); J(τ + a ) ) = [∆h (Φ (q)) eWΦ(q) (x)∆h (Φ (q)) ] ×[∆h (Φ (q)) eWΦ(q) (a)∆h (Φ (q)) ]−1(18) = W (x)W (a) (19) where in the first equality we understand WΦ(q)(x) to be the scale function associate”
Evaluating Scale Functions of Spectrally Negative Lévy Processes (2008, background): “We refer the reader to [16] for further discussions.”
Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory (2011, background): “(3.14) Moreover, using a fact in Kyprianou and Palmowski (2005) we get P (Φ(β)) −z (T−b ∞) = 1− ϕ ′ Φ(β)(0+)WΦ(β)(b− z).”
Valuing equity-linked death benefits and other contingent options: A discounted density approach (2012, background): “See also Section 4 in Kyprianou and Palmowski (2005).”