scholarly journals On Multivariate Vernic Recursions

2000 ◽  
Vol 30 (1) ◽  
pp. 111-122 ◽  
Author(s):  
Bjørn Sundt
Keyword(s):  
Recursive Algorithm ◽  
Compound Distributions ◽  
Counting Distribution

AbstractIn the present paper we extend a recursive algorithm developed by Vernic (1999) for compound distributions with bivariate counting distribution and univariate severity distributions to more general multivariate counting distributions.

scholarly journals A Recursive Procedure for Calculation of some Compound Distributions

1994 ◽  
Vol 24 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Ole Hesselager
Keyword(s):  
Poisson Process ◽  
Recursive Algorithm ◽  
Recursive Procedure ◽  
Probability Of Ruin ◽  
Compound Distributions ◽  
Compound Distribution ◽  
Counting Distribution ◽  
Mixed Poisson Process ◽  
The One

AbstractWe consider compound distributions where the counting distribution has the property that the ratio between successive probabilities may be written as the ratio of two polynomials. We derive a recursive algorithm for the compound distribution, which is more efficient than the one suggested by Panjer & Willmot (1982) and Willmot & Panjer (1987). We also derive a recursive algorithm for the moments of the compound distribution. Finally, we present an application of the recursion to the problem of calculating the probability of ruin in a particular mixed Poisson process.

scholarly journals Further Results on Recursive Evaluation of Compound Distributions

1981 ◽  
Vol 12 (1) ◽  
pp. 27-39 ◽  
Author(s):  
Bjørn Sundt ◽  
William S. Jewell
Keyword(s):  
Recent Result ◽  
Recursive Algorithm ◽  
Compound Distributions ◽  
Compound Distribution ◽  
Aggregate Claims ◽  
Recursive Evaluation

A recent result by Panjer provides a recursive algorithm for the compound distribution of aggregate claims when the counting law belongs to a special recursive family. In the present paper we first give a characterization of this recursive family, then describe some generalizations of Panjer's result.

ON THE EVALUATION OF MULTIVARIATE COMPOUND DISTRIBUTIONS WITH CONTINUOUS SEVERITY DISTRIBUTIONS AND SARMANOV'S COUNTING DISTRIBUTION

2018 ◽  
Vol 48 (02) ◽  
pp. 841-870 ◽  
Author(s):  
Maissa Tamraz ◽  
Raluca Vernic
Keyword(s):  
Distribution Function ◽  
Hypergeometric Function ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Type Ii ◽  
Similar Function ◽  
Compound Distributions ◽  
Closed Type ◽  
Counting Distribution

AbstractIn this paper, we present closed-type formulas for some multivariate compound distributions with multivariate Sarmanov counting distribution and independent Erlang distributed claim sizes. Further on, we also consider a type-II Pareto dependency between the claim sizes of a certain type. The resulting densities rely on the special hypergeometric function, which has the advantage of being implemented in the usual software. We numerically illustrate the applicability and efficiency of such formulas by evaluating a bivariate cumulative distribution function, which is also compared with the similar function obtained by the classical recursion-discretization approach.

scholarly journals Recursive Evaluation of Some Bivariate Compound Distributions

1999 ◽  
Vol 29 (2) ◽  
pp. 315-325 ◽  
Author(s):  
Raluca Vernic
Keyword(s):  
Probability Function ◽  
Bivariate Distribution ◽  
Compound Distributions ◽  
Counting Distribution ◽  
Image Position ◽  
Recursive Evaluation

AbstractIn this paper we consider compound distributions where the counting distribution is a bivariate distribution with the probability function (Pn1,n2)n1,n2≥0 that satisfies a recursion in the formWe present an algorithm for recursive evaluation of the corresponding compound distributions and some examples of distributions in this class.

scholarly journals Further Results on Hesselager's Recursive Procedure for Calculation of some Compound Distributions

1994 ◽  
Vol 24 (2) ◽  
pp. 161-166 ◽  
Author(s):  
Shaun Wang ◽  
Monica Sobrero
Keyword(s):  
General Class ◽  
Recursive Algorithm ◽  
Recursive Procedure ◽  
Compound Distributions ◽  
Poisson Distributions

AbstractThe recursive algorithm of Hesselager (1994) is extended to a more general class of counting distributions, which includes Sundt's (1992) class as well as all the mixed Poisson distributions discussed by Willmot (1993).

scholarly journals On Error Bounds for Approximations to Aggregate Claims Distributions

1997 ◽  
Vol 27 (2) ◽  
pp. 243-262 ◽  
Author(s):  
Jan Dhaene ◽  
Bjørn Sundt
Keyword(s):  
Error Bounds ◽  
Compound Distributions ◽  
Counting Distribution ◽  
Aggregate Claims

AbstractIn the present paper we discuss error bounds for approximations to aggregate claims distributions. We consider approximations to convolutions by approximating each of the distributions and taking the convolution of these approximations. For compound distributions we consider two classes of approximations. In the first class we approximate the counting distribution, but keep the severity distribution unchanged, whereas in the second class we approximate the severity distribution, but keep the counting distribution unchanged. We finally look at some examples.

scholarly journals Recursions for certain bivariate counting distributions and their compound distributions

1996 ◽  
Vol 26 (1) ◽  
pp. 35-52 ◽  
Author(s):  
Ole Hesselager
Keyword(s):  
Recursive Algorithm ◽  
Compound Distributions ◽  
Compound Distribution

AbstractWe consider three classes of bivariate counting distributions and the corresponding compound distributions. For each class we derive a recursive algorithm for calculating the bivariate compound distribution.

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