Tail Moments of Compound Distributions

2021 ◽  
Author(s):  
Jiandong Ren
Keyword(s):  
Compound Distributions

Recursions and Fast Fourier Transforms for Certain Bivariate Compound Distributions

2010 ◽  
Vol 5 (4) ◽  
pp. 19-33 ◽  
Author(s):  
Tao Jin ◽  
Jiandong Ren
Keyword(s):  
Fourier Transforms ◽  
Fast Fourier Transforms ◽  
Compound Distributions

A simulation comparison of quantile approximation techniques for compound distributions popular in operational risk

2016 ◽  
Vol 11 (1) ◽  
pp. 23-48 ◽  
Author(s):  
P. J. de Jongh ◽  
Tertius de Wet ◽  
Kevin Panman ◽  
Helgard Raubenheimer
Keyword(s):  
Operational Risk ◽  
Compound Distributions ◽  
Approximation Techniques ◽  
Quantile Approximation

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.

Some recursions for moments of compound distributions

2003 ◽  
Vol 33 (3) ◽  
pp. 487-496 ◽  
Author(s):  
Bjørn Sundt
Keyword(s):  
Compound Distributions

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 Modified Recursions for a Class of Compound Distributions

1996 ◽  
Vol 26 (2) ◽  
pp. 213-224 ◽  
Author(s):  
Karl-Heinz Waldmann
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Mass Function ◽  
Cumulative Distribution ◽  
Probability Mass Function ◽  
Initial Value ◽  
Compound Distributions ◽  
Claim Frequency ◽  
Probability Mass ◽  
Stop Loss

AbstractRecursions are derived for a class of compound distributions having a claim frequency distribution of the well known (a,b)-type. The probability mass function on which the recursions are usually based is replaced by the distribution function in order to obtain increasing iterates. A monotone transformation is suggested to avoid an underflow in the initial stages of the iteration. The faster increase of the transformed iterates is diminished by use of a scaling function. Further, an adaptive weighting depending on the initial value and the increase of the iterates is derived. It enables us to manage an arbitrary large portfolio. Some numerical results are displayed demonstrating the efficiency of the different methods. The computation of the stop-loss premiums using these methods are indicated. Finally, related iteration schemes based on the cumulative distribution function are outlined.

Compound distributions

2001 ◽  
pp. 51-80 ◽  
Author(s):  
Gordon E. Willmot ◽  
X. Sheldon Lin
Keyword(s):  
Compound Distributions

scholarly journals Compound distributions for financial returns

PLoS ONE ◽  
2020 ◽  
Vol 15 (10) ◽  
pp. e0239652
Author(s):  
Emmanuel Afuecheta ◽  
Artur Semeyutin ◽  
Stephen Chan ◽  
Saralees Nadarajah ◽  
Diego Andrés Pérez Ruiz
Keyword(s):  
Financial Returns ◽  
Compound Distributions

scholarly journals Computing Moments of Compound Distributions

1986 ◽  
pp. 381-384
Author(s):  
R. Kaas ◽  
M. J. Goovaerts
Keyword(s):  
Compound Distributions
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