The multivariate De Pril transform

Sundt, Bjørn

doi:10.1016/s0167-6687(00)00041-x

Cited by 16 publications

(15 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The recursions of the present subsection are further analysed in Sundt (1998 4A. We consider the situation where a claim event can induce various types of claims, and assume that one claim event cannot induce claims of more than one type.…”

Section: )'mentioning

confidence: 99%

On Multivariate Panjer Recursions

Sundt

1999

ASTIN Bull.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: )'mentioning

confidence: 99%

On Multivariate Panjer Recursions

Sundt

1999

ASTIN Bull.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hipp's r-th order approximation is defined by restricting the summations over k in (32) to summations over all k values smaller than or equal to r with r some positive integer. The recursion that arises is of the form (26) with…”

Section: By Easier Computable Values H(x)mentioning

confidence: 99%

“…A general framework for recursions of both the individual and collective risk models is introduced and explored in Sundt [30,31,32] and Sundt, Dhaene, De Pril [35] . An extended survey of the literature on recursive evaluation of aggregate claims distributions is given in Sundt [34] .…”

Section: Introductionmentioning

confidence: 99%

Recursions for the Individual Risk Model

Dhaene

Ribas

Vernic

2006

Acta Math. Appl. Sin, Engl. Ser.

View full text Add to dashboard Cite

In the actuarial literature, several exact and approximative recursive methods have been proposed for calculating the distribution of a sum of mutually independent compound Bernoulli distributed random variables. In this paper, we give an overview of these methods. We compare their performance with the straightforward convolution technique by counting the number of dot operations involved in each method. It turns out that in many practicle situations, the recursive methods outperform the convolution method.

show abstract

“…Since Panjer (1981), many recursive algorithms have been derived from compound distributions with univariate counting distribution (see Willmot, 1986;Willmot and Panjer, 1987;Panjer and Willmot, 1992;Sundt, 1992;Willmot, 1993;Hesselager, 1994;and others) and also for bi-and multivariate distributions (see Hesselager, 1996;Ambagaspitiya, 1998;Sundt, 1998aSundt, , b, 1999a. Hesselager (1996) presented some bivariate extensions of Panjer's recursion, using bivariate generalisations of the counting distribution.…”

Section: Y=\mentioning

confidence: 99%