Lundberg Approximations for Compound Distributions With Insurance Applications

By Tomasz Rolski. 2002

101 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/32495d17ebb06c075a2eaafe96a2be942956f003

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Citations in the corpus

On the discounted penalty function in the renewal risk model with general interclaim times (2007, background): “…when (2.15) holds with k = 1 and r = 2 (e.g. Tijms, 1994, pp. 360-361), and for this class (2.14) is of the form Gδ(u) = c1,δe −R1,δu + c2,δe −R2,δu, (2.18) and (2.18) is also the form of the Tijms approximation to the compound geometric tail Gδ(u) itself (Willmot and Lin, 2001, Chapter 8).”
Ruin Probabilities in the Compound Markov Binomial Model (2003, unknown): “Willmot & Lin (2001) obtain compound geometric bounds and asymptotic approximations for the infinite-time ruin probabilities.”
On the Density and Moments of the Time of Ruin with Exponential Claims (2003, background): “The Laplace transform of the (defective) distribution of the time to ruin satisfies the so-called Gerber-Shiu defective renewal equation, and is well known to be the tail of a compound geometric distribution (e.g. Willmot and Lin, 2001, Section 9.2).”
An Extension of Panjer's Recursion (2002, unknown): “• Willmot (1988) used the term extended truncated negativebinomial distribution for ENB(1, β, ϑ) ; see also Klugman, Panjer and Willmot (1998) and Willmot and Lin (2001).”
Compound geometric residual lifetime distributions and the deficit at ruin (2002, background): “The following result is very similar to that which holds for the classical model (Willmot and Lin, 2001, pp. 188-9).”
On the Class of Erlang Mixtures with Risk Theoretic Applications (2007, background): “…the residual lifetime distribution, the equilibrium or integrated tail distribution, the aggregate claims distribution, and the conditional distribution of the deficit at ruin (given that ruin occurs) are all different mixtures of the same Erlangs (e.g., Willmot 2000; Willmot and Lin 2001).”
Modeling and Evaluating Insurance Losses Via Mixtures of Erlang Distributions (2010, methodology): “…with common scale parameter can be expressed as a compound distribution with its secondary distribution being exponential, any quantiles and excess loss distributions (i.e., cost per payment distributions) can be written as damped exponential series (e.g. Willmot and Lin 2001, pp. 20–21).”