Randomized observation periods for the compound Poisson risk model: the discounted penalty function

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Exit identities for L\'evy processes observed at Poisson arrival times (2014, background): “Quantities related to T− 0 have been studied for a compound Poisson risk model in [2], and in [15] a simple formula for Px(T 0 < ∞) was established for general spectrally-negative Lévy processes X(t).”
Randomized Observation Periods for the Compound Poisson Risk Model: Dividends (2011, methodology): “[1], we will investigate the expected discounted penalty function (Gerber & Shiu [9]) under random observation times.”
The Joint Laplace Transforms for Diffusion Occupation Times (2013, background): “Unfortunately, it is not apparent that the ruin probability for this general risk model with Erlang(n) interarrival times in [2] and [3] can be associated to the occupation times in a nice way due to the lack-of-memoryless property.”
Valuing equity-linked death benefits and other contingent options: A discounted density approach (2012, methodology): “For more applications of the method, see Albrecher et al. (2012). 17”
The Omega model: from bankruptcy to occupation times in the red (2012, background): “[3], dos Reis [5], Loisel [9] and Zhang and Wu [11].”