On a general class of renewal risk process: analysis of the Gerber-Shiu function

By Shuanming Li, José Garrido. Advances in Applied Probability, 2005

103 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/497f7aa634ca66e66362052a0a74481528b38016

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Citations in the corpus

On the discounted penalty function in the renewal risk model with general interclaim times (2007, methodology): “The mixture representation (2.8) implies that the ladder height pdf fδ(y) is from the same family of distributions as p(y) in many cases.”
On a risk model with dependence between interclaim arrivals and claim sizes (2006, methodology): “…with the discounted penalty function has been proposed by Gerber and Shiu (1998) in the framework of the compound Poisson risk model and has been then studied for some classes of the Sparre Andersen risk model (see Dickson and Hipp (2001), Gerber and Shiu (2005) and Li and Garrido (2004, 2005)).”
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).”
The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model (2007, background): “…when the distribution function of interclaim waiting times is (a) Erlang(2) (Dickson and Hipp 1998; Cheng and Tang 2003; Lin 2003); (b) Erlang (n) (Li and Garrido 2004); (c) phase-type (2) (Dickson and Hipp 2001; Dickson and Drekic 2004); (d) convolution of n exponential distribution (Gerber and…”
On the discounted penalty function in a Markov-dependent risk model (2005, unknown): “ω̃(s) = 1−b̃(a+s) a+s , and from (21) E(e − Tx 1{Tx<∞}) = λ c− λμ (”
Randomized observation periods for the compound Poisson risk model: the discounted penalty function (2013, background): “…with Equation (3.1) for x 0 and w(x1, x2) e r1x1 r2x2 establishes h 2;dðz; yj0Þ ¼ Xn i¼1 Wie ai zgd;þðzþ yÞ; z; y > 0: (3.27) Note that the form of Equation (3.27) resembles Equation (16) of Li & Garrido (2005) for the classical Sparre Andersen risk model with Coxian interclaim time distribution.”
Dependent Risk Models with Bivariate Phase-Type Distributions (2009, background): “We remind the reader that the discounted density of the surplus prior to ruin and the deficit at ruin has been studied by many authors in ruin theory (see, e.g. Gerber and Shiu (1997), Li and Garrido (2005), and Ren (2007)).”