On ruin for the Erlang(n) risk process

By Shuanming Li, José Garrido. 2004

287 citations recorded by the source corpus.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/4a9c736df72340462d060d64874018bf2c1a7eb7

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Citations in the corpus

On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula (2008, methodology): “(35) Based on Lemma 1 on page 395 (and also on the relations on page 400) of Li and Garrido (2004), the terms summed on the indices j in (35) are equal to zero except for l = 0, for which it sums to σ0 and the last term, for l = c+2, for whichwe obtain −σc+2 τc+2(0) .”
On the joint distribution of surplus before and after ruin under a Markovian regime switching model (2006, background): “Li and Garrido [10] obtained the closed form solution of the infinite-horizon ruin probability and the joint distribution of the surplus before and after ruin for the Sparre Andersen models when the initial surplus is zero or the claim sizes belong to the rational family which includes the phase-typ”
The compound Poisson risk model with a threshold dividend strategy (2006, methodology): “Section 2 recalls properties of the translation operator, first employed for risk processes by Dickson and Hipp (2001) and recently discussed by Li and Garrido (2004a) and Gerber and Shiu (2005b).”
The Gerber–Shiu function in a Sparre Andersen risk process perturbed by diffusion (2005, background): “Next, as in [16], we define the operator Tr of a real-valued function f, with respect to a complex number r as: Tr f (x) g x e r(y f (y)dy; x]0: There is a close connection between divided differences and the operator Tr.”
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): “Proof: Equations (11) can be written as Expanding the determinant in the numerator along the i -th column then yields the desired result.”
On a risk model with dependence between interclaim arrivals and claim sizes (2006, methodology): “…s2 h̃2;d(s2) s2 1 s2 s1 h̃2;d(s1) s s2 s1 s2 h̃2;d(s2) s s1 s2 s1 : Therefore, using Property 6 of the Dickson-Hipp operator on page 394 of Li and Garrido (2004), h̃1;d(s) h̃2;d(s) on the right-hand side of (14) becomes h̃1;d(s) h̃2;d(s) h̃1;d(0) (s s1)(s s2) s1s2 (s s1)(s…”
Analysis of ruin measures for the classical compound Poisson risk model with dependence (2010, methodology): “…we use the Dickson Hipp operator Tr for an integrable real-valued function f (introduced by Dickson & Hipp (2001)) defined by Trf (x) g x e r(u x)f (u)du; r C: Li & Garrido (2004) provide a list of properties of the operator Tr and we recall three of them that will be useful for us: (1) Property 1.”
An Insurance Risk Model with Parisian Implementation Delays (2013, unknown): “Among others, the well-known Dickson–Hipp operator in ruin theory (see, e.g., Li and Garrido 2004) and Bell’s polynomials in combinatorial theory (see, e.g., Riordan 1980) will be used to carry out the analysis.”