Recursions for certain bivariate counting distributions and their compound distributions

Hesselager, Ole

doi:10.2143/ast.26.1.563232

Cited by 46 publications

(48 citation statements)

References 10 publications

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“…We are now within Model A of Hesselager (1996), and the recursions (4.5) and (4.8) are given in his Theorems 2.2 and 2.1 respectively.…”

Section: Fmentioning

confidence: 99%

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On Multivariate Panjer Recursions

Sundt

1999

ASTIN Bull.

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In the present paper we generalise Panjer's (1981) recursion for compound distributions to a multivariate situation where each claim event generates a random vector. We discuss situations within insurance where such models could be applicable, and consider some special cases of the general algorithm. Finally we deduce from the algorithm a multivariate extension of De Pril's (1985) recursion for convolutions.

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“…We are now within Model A of Hesselager (1996), and the recursions (4.5) and (4.8) are given in his Theorems 2.2 and 2.1 respectively.…”

Section: Fmentioning

confidence: 99%

“…Hesselager (1996) presented some bivariate extensions of Panjer's recursion, using bivariate generalisations of the counting distribution. He considered a situation with two portfolios.…”

mentioning

confidence: 99%

On Multivariate Panjer Recursions

Sundt

1999

ASTIN Bull.

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“…The distribution of the vector X = (X 1 , X 2 ) is recovered through a recursion procedure in [4,24], whereas the distribution of the vector Y = (Y 1 , Y 2 ) is studied in [12,24,26]. Recursion based techniques rely on the existence of recurrence relationships between the probabilities of the claim frequencies which limits their use to certain kind of distributions.…”

Section: Introductionmentioning

confidence: 99%

Polynomial Approximations for Bivariate Aggregate Claims Amount Probability Distributions

Goffard¹,

Loisel²,

Pommeret³

2015

Methodol Comput Appl Probab

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A numerical method to compute bivariate probability distributions from their Laplace transforms is presented. The method consists in an orthogonal projection of the probability density function with respect to a probability measure that belongs to a Natural Exponential Family with Quadratic Variance Function (NEF-QVF). A particular link to Lancaster probabilities is highlighted. The procedure allows a quick and accurate calculation of probabilities of interest and does not require strong coding skills. Numerical illustrations and comparisons with other methods are provided. This work is motivated by actuarial applications. We aim at recovering the joint distribution of two aggregate claims amounts associated with two insurance policy portfolios that are closely related, and at computing survival functions for reinsurance losses in presence of two non-proportional reinsurance treaties.

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“…In a different context, Hipp showed in Hipp (2006) that Panjer's recursion is reduced to one of a local depth if the severity distributions are of phase type. For a long time, Panjer's recursion principle has been generalized to various multivariate cases (see Hesselager (1996), Sundt (1999), Vernic (1999), Sundt (2000) and the forthcoming extensive book by Sundt and Vernic (in press)). Using the ideas in Eisele (2006), it is therefore obvious to look for recursion formulas for multivariate compound phase variables.…”

Section: Introductionmentioning

confidence: 99%