On the time to ruin for Erlang(2) risk processes

By D. Dickson, Christian Hipp. 2001

286 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/04626db5160f598e50a76e3e54f50f4491b7625a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process (2003, methodology): “(1.1) The Erlang(2) risk model has been investigated by Dickson (1998) and Dickson and Hipp (2000, 2001).”
On a risk model with dependence between interclaim arrivals and claim sizes (2006, methodology): “Using the Dickson-Hipp operator Tr defined as Tr f (u) g u e r(y u)f (y) dy; (9) (see Dickson and Hipp (2001) and Li and Garrido (2004)), (9) can be rewritten as md(u) l c Tl d b c s1;d(u) Tl d b c s2;d(u) Tl d c s2;d(u) !”
Randomized observation periods for the compound Poisson risk model: the discounted penalty function (2013, methodology): “Here we have used the fact that the Dickson Hipp operator satisfies T s1T s2 f ðyÞ ¼ T s2T s1 f ðyÞ ¼ T s1 f ðyÞ T s2 f ðyÞ s2 s1 ; y 0 (3.12) for all complex numbers s1 " s2 (see e.g. Li & Garrido 2004, Sec.”
On a class of discrete time renewal risk models (2005, background): “(8) Equation (8) is a generalized version of Lundberg equation.”
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 Density of the Time to Ruin in the Classical Poisson Risk Model (2005, unknown): “From Dickson and Hipp (2001) we know that ∫ ∞ 0 ehρ(u)du = p̃(ρ)− p̃(s) s− ρ so that for n = 1, 2, 3, .”
The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model (2007, background): “…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 Shiu 2005a); (e) phase-type (Schmidli…”
The Decompositions of the Discounted Penalty Functions and Dividends-Penalty Identity in a Markov-Modulated Risk Model (2008, methodology): “This operator has been used for the integrable real-valued function in some papers, see, for example, Dickson and Hipp (2001) and Li and Garrido (2004).”
On the discounted penalty function in a Markov-dependent risk model (2005, unknown): “,M) are given by C (i) j1,j2 = (−1)2 · detKj2,i · ∑M l=1 λl pl,j1kj2,l c detK (13) with kj2,l denoting the l-th component of vector kj2 (l=1,.”
Analysis of ruin measures for the classical compound Poisson risk model with dependence (2010, methodology): “For that purpose, we use the Dickson–Hipp operator T r for an integrable real-valued function f (introduced by Dickson & Hipp ( 2001 )) defined by”
On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula (2008, methodology): “(24) In what follows, we use the Dickson–Hipp operator Tr for an integrable real-valued function f introduced by Dickson and Hipp (2001): Tr f (x) = ∫ ∞ x e−r(u−x)f (u)du, r ∈ C. (25) From Li and Garrido (2004), we recall properties 1, 2, and 6 of the operator Tr that we use in what follows: •…”