Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process

A note on ruin problems in perturbed classical risk models

“…A nice formula for ω u (n, t) in the classical risk model without perturbation (i.e., σ = 0) has been discussed in Dickson (2012). For other related results we refer to Egídio dos Reis (2002), Borovkov and Dickson (2008), Landriault et al (2011), Lee (2011), Frostig et al (2012, Zhao and Zhang (2013), Cheung (2013), Li et al (2013), Landriault and Shi (2014) and Li et al (2016). It is noted that in most of the aforementioned papers with r ∈ (0, 1], δ > 0 andp the Laplace transform of p. We note in passing that the above Lundberg fundamental equation was derived in Landriault et al (2011) by introducing the following quantity…”

“…in Dickson (2012). For other related results we refer to Egídio dos Reis (2002), Borovkov and Dickson (2008), Landriault et al (2011), Lee (2011), Frostig et al (2012, Zhao and Zhang (2013), Cheung (2013), Li et al (2013), Landriault and Shi (2014) and Li et al (2016). It is noted that in most of the aforementioned papers results are obtained based on an application of the known Lagrange's Expansion Theorem.…”

The distribution of some extremum on the risk process whose income depend on the current reserve

“…Among others, we only mention a few, for example Dickson and Li (2013), Gerber (1990), Gerber and Shiu (1998), Zacks (2007), Xu (2012), Kyprianou (2013), Landriault and Shi (2014), Li and Lu (2014), Li et al. (2015) and references therein.…”