scholarly journals The Aggregate Claims Distribution in the Individual Model with Arbitrary Positive Claims

1989 ◽  
Vol 19 (1) ◽  
pp. 9-24 ◽  
Author(s):  
Nelson De Pril
Keyword(s):  
Computing Time ◽  
Recursion Formula ◽  
Theory Model ◽  
Risk Theory ◽  
Individual Risk ◽  
Present Contribution ◽  
Individual Model ◽  
Life Model ◽  
Aggregate Claims ◽  
The Individual

AbstractIn an earlier paper the author derived a recursion formula which permits the exact computation of the aggregate claims distribution in the individual life model. To save computing time he also proposed an approximative procedure based on the exact recursion.In the present contribution the exact recursion formula and the related approximations are generalized to the individual risk theory model with arbitrary positive claims. Error bounds for the approximations are given and it is shown that they are smaller than those of the Kornya-type approximations.

scholarly journals On the Exact Computation of the Aggregate Claims Distribution in the Individual Life Model

1986 ◽  
Vol 16 (2) ◽  
pp. 109-112 ◽  
Author(s):  
Nelson De Pril
Keyword(s):  
Life Insurance ◽  
Approximation Method ◽  
Recursion Formula ◽  
Exact Computation ◽  
Individual Model ◽  
Individual Life ◽  
Insurance Policies ◽  
Life Model ◽  
Aggregate Claims ◽  
The Individual

AbstractA recursive expression is derived for computing exactly the distribution of aggregate claims of a portfolio of life insurance policies. The recursion generalizes a formula of White and Greville for the claim numbers distribution and improves Kornya's approximation method for the aggregate claims distribution. It can be seen as the counterpart in the individual model of Panjer's recursion formula for the collective model.

scholarly journals Error Bounds for Compound Poisson Approximations of the Individual Risk Model

1992 ◽  
Vol 22 (2) ◽  
pp. 135-148 ◽  
Author(s):  
Nelson De Pril ◽  
Jan Dhaene
Keyword(s):  
Risk Model ◽  
General Setting ◽  
Poisson Model ◽  
Individual Risk ◽  
Compound Poisson ◽  
Aggregate Claims ◽  
The Individual ◽  
Stop Loss ◽  
Work Done

AbstractThe approximation of the individual risk model by a compound Poisson model plays an important role in computational risk theory. It is thus desirable to have sharp lower and upper bounds for the error resulting from this approximation if the aggregate claims distribution, related probabilities or stop-loss premiums are calculated.The aim of this paper is to unify the ideas and to extend to a more general setting the work done in this connection by Bühlmann et al. (1977), Gerber (1984) and others. The quality of the presented bounds is discussed and a comparison with the results of Hipp (1985) and Hipp & Michel (1990) is made.

scholarly journals Improved Approximations for the Aggregate Claims Distribution in the Individual Model

1986 ◽  
Vol 16 (2) ◽  
pp. 89-100 ◽  
Author(s):  
Christian Hipp
Keyword(s):  
Error Bounds ◽  
Absolute Error ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
Individual Model ◽  
Concentration Functions ◽  
Aggregate Claims ◽  
The Individual ◽  
Stop Loss

AbstractKornya-type higher order approximations are derived for the aggregate claims distribution and for stop loss premiums in the individual model with arbitrary positive claims. Absolute error bounds and error bounds based on concentration functions are given. In the Gerber portfolio containing 31 policies, second order approximations lead to an accuracy of 3 × 10−4, and third order approximations to 1.7 ×10−5.

scholarly journals On the Exact Calculation of the Aggregate Claims Distribution in the Individual Life Model

1994 ◽  
Vol 24 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Karl-Heinz Waldmann
Keyword(s):  
Iteration Scheme ◽  
Numerical Results ◽  
Exact Calculation ◽  
Scaling Functions ◽  
Arithmetic Operations ◽  
Individual Life ◽  
Exact Procedure ◽  
Life Model ◽  
Aggregate Claims ◽  
The Individual

AbstractAn iteration scheme is derived for calculating the aggregate claims distribution in the individual life model. The (exact) procedure is an efficient reformulation of De Pril's (1986) algorithm, considerably reducing both the number of arithmetic operations to be carried out and the number of data to be kept at each step of iteration. Scaling functions are used to stabilize the algorithm in case of a portfolio with a large number of policies. Some numerical results are displayed to demonstrate the efficiency of the method.

scholarly journals Pseudo Compound Poisson Distributions in Risk Theory

1990 ◽  
Vol 20 (1) ◽  
pp. 57-79 ◽  
Author(s):  
W. Hürlimann
Keyword(s):  
Risk Theory ◽  
Continuous Case ◽  
Infinitely Divisible ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Life Model ◽  
Numerical Tools ◽  
The Individual ◽  
Finite Sum ◽  
Analytical Expressions

AbstractUsing Laplace transforms and the notion of a pseudo compound Poisson distribution, some risk theoretical results are revisited. A well-known theorem by Feller (1968) and Van Harn (1978) on infinitely divisible distributions is generalized. The result may be used for the efficient evaluation of convolutions for some distributions. In the particular arithmetic case, alternate formulae to those recently proposed by De Pril (1985) are derived and shown more adequate in some cases. The individual model of risk theory is shown to be pseudo compound Poisson. It is thus computable using numerical tools from the theory of integral equations in the continuous case, a formula of Panjer type or the Fast Fourier transform in the arithmetic case. In particular our results contain some of De Pril's (1986/89) recursive formulae for the individual life model with one and multiple causes of decrement. As practical illustration of the continuous case we construct a new two-parametric family of claim size density functions whose corresponding compound Poisson distributions are analytical finite sum expressions. Analytical expressions for the finite and infinite time ruin probabilities are also derived.

scholarly journals Suicide Related Phenotypes in a Bipolar Sample: Genetic Underpinnings

Genes ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1482
Author(s):  
Line K. M. Lybech ◽  
Marco Calabró ◽  
Silvana Briuglia ◽  
Antonio Drago ◽  
Concetta Crisafulli
Keyword(s):  
Pathway Analysis ◽  
Individual Risk ◽  
Worth Living ◽  
Present Contribution ◽  
Molecular Pathway ◽  
Molecular Events ◽  
Genome Wide ◽  
Significant Enrichment ◽  
The Individual ◽  
Suicide Behaviors

Suicide in Bipolar Disorder (BD) is a relevant clinical concern. Genetics may shape the individual risk for suicide behavior in BD, together with known clinical factors. The lack of consistent replication in BD may be associated with its multigenetic component. In the present contribution we analyzed a sample of BD individuals (from STEP-BD database) to identify the genetic variants potentially associated with three different suicide-related phenotypes: 1) a feeling that the life was not worth living; 2) fantasies about committing a violent suicide; 3) previous attempted suicide. The sample under analysis included 1115 BD individuals. None of the SNPs reached genome-wide significance. However, a trend of association was evidenced for rs2767403, an intron variant of AOPEP gene, in association with phenotype #1 (p = 5.977 × 10−6). The molecular pathway analysis showed a significant enrichment in all the investigated phenotypes on pathways related to post synaptic signaling, neurotransmission and neurodevelopment. Further, NOTCH signaling or the γ-aminobutyric acid (GABA) -ergic signaling were found to be associated with specific suicide-related phenotypes. The present investigation contributes to the hypothesis that the genetic architecture of suicide behaviors in BD is related to alteration of entire pathways rather than single genes. In particular, our molecular pathway analysis points on some specific molecular events that could be the focus of further research in this field.

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