On the Evaluation of Some Multivariate Compound Distributions with Sarmanov's Counting Distribution

2016 ◽  
Author(s):  
Raluca Vernic
Keyword(s):  
Compound Distributions ◽  
Counting Distribution

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.

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 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 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.

On a generalization of the Rényi–Srivastava characterization of the Poisson law

2021 ◽  
Vol 58 (1) ◽  
pp. 68-82
Author(s):  
Jean-Renaud Pycke
Keyword(s):  
Life Insurance ◽  
Collective Model ◽  
New Method ◽  
Bell Polynomials ◽  
Explicit Formulas ◽  
Compound Distributions ◽  
Poisson Law ◽  
Pierre Loti

AbstractWe give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson law due to Rényi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.

scholarly journals Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting

1999 ◽  
Vol 29 (2) ◽  
pp. 197-214 ◽  
Author(s):  
Rudolf Grübel ◽  
Renate Hermesmeier
Keyword(s):  
Numerical Evaluation ◽  
Change Of Measure ◽  
Exponential Tilting ◽  
Transform Methods ◽  
Compound Distributions ◽  
Heavy Tailed Distributions ◽  
Panjer Recursion ◽  
Heavy Tailed ◽  
Suitable Change

AbstractNumerical evaluation of compound distributions is one of the central numerical tasks in insurance mathematics. Two widely used techniques are Panjer recursion and transform methods. Many authors have pointed out that aliasing errors imply the need to consider the whole distribution if transform methods are used, a potential drawback especially for heavy-tailed distributions. We investigate the magnitude of aliasing errors and show that this problem can be solved by a suitable change of measure.

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