Passage times for a spectrally negative Lévy process with applications to risk theory

By Sung Nok Chiu, Chuancun Yin. 2005

69 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4a4f2c823473c1dd6ec0856e8a57eb1c97f9072e

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Citations in the corpus

A Lévy Insurance Risk Process with Tax (2008, unknown): “[6], [8], [9], [11], [13], and [18].”
Fluctuations of spectrally negative Markov additive processes (2008, background): “Replacing (10) and (12) in (11) and considering the latter vector equality as the i-th row of a matrix, we obtain”
On The Expected Discounted Penalty function for Lévy Risk Processes (2006, background): “Chiu and Yin (2005) study the last time that the risk process crosses level zero, as well as the duration of the ruin event.”
Smoothness of scale functions for spectrally negative Lévy processes (2009, unknown): “Then the solution of the renewal equation (8) is unique in the class of functions which are bounded on bounded intervals and has the form f(x) = ∑ n≥0 g (x) on any interval [0, a).”
Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “…(2004) and Bekker et al. (2007), in the theory of branching processes Bingham (1976) and Lambert (2007), in the theory of insurance risk and ruin Chiu and Yin (2005), Klüppelberg et al. (2004), Klüppelberg and Kyprianou (2006), Doney and Kyprianou (2006), Kyprianou and Palmowski (2007),…”
Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory (2011, background): “For x ≥ 0, q > 0, β > 0, it follows from Theorem 3.2 in Chiu and Yin (2005) we have Ex(e −qT−β(l−T ), T ∞) = ϕ′(0+)Φ′(β)eΦ(β)x ( Z (p) Φ(β)(x)− p ΦΦ(β)(p) W (p) Φ(β)(x) ) .”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, unknown): “In the context of last ruin times Chiu and Yin (2005) and Baurdoux (2008) also make extensive use of the theory of scale functions.”
Fluctuations of Lévy Processes with Applications (2014, methodology): “This exercise is based on the results of Chiu and Yin (2005). Suppose that X is any spectrally negative Lévy process with Laplace exponent ψ, satisfying limt↑∞Xt = ∞.”