On the discounted penalty function in the renewal risk model with general interclaim times

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Dependent Risk Models with Bivariate Phase-Type Distributions (2009, background): “We remark that (26) can also be retrieved from Ahn and Ramaswami (2005, Theorem 3) with s = 0 by recalling that the ruin probability for the surplus process R and the probability that the fluid process F ∗ eventually hits level 0 at least once coincide.”
An Insurance Risk Model with Parisian Implementation Delays (2013, unknown): “…actuarial risk theory, a lot of attention has been given to the analysis of events related to the time of default which is assumed to occur if and when the surplus process falls below a certain threshold level for the first time (see, e.g., Gerber and Shiu 1998; Li and Garrido 2005; Willmot 2007).”
Randomized observation periods for the compound Poisson risk model: the discounted penalty function (2013, unknown): “Consequently, from Equation (3.27), h 2;dðz; yj0Þ ¼ cðn RcÞðqc q0Þ cðqc þ RcÞ e ðRcþq0Þz Rcy; z; y > 0: Suppose now wðx1; x2Þ ¼ e r1x1 w2ðx2Þ (see e.g. Willmot 2007).”