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.

On a Dual Model with Multi-Layer Dividend Strategy under Stochastic Interest

2011 ◽  
Vol 422 ◽  
pp. 775-778
Author(s):  
Jin Sheng Yin
Keyword(s):  
Differential Equations ◽  
Poisson Model ◽  
Dual Model ◽  
Exponential Distributions ◽  
Compound Poisson ◽  
Compound Poisson Model ◽  
Surplus Process ◽  
Stochastic Interest ◽  
Aggregate Claims

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual model of the compound Poisson model with multi-layer dividend strategy under stochastic interest. We derive a set of integro-differential equations satisfied by the expected total discounted dividends until ruin. The cases where profits follow an exponential distributions are solved.

scholarly journals A Functional Approach to Approximations for the Individual Risk Model

2004 ◽  
Vol 34 (2) ◽  
pp. 379-397 ◽  
Author(s):  
Susan M. Pitts
Keyword(s):  
Negative Binomial ◽  
Risk Model ◽  
Order Approximation ◽  
Functional Approach ◽  
Individual Risk ◽  
Claim Amount ◽  
Total Claim Amount ◽  
Total Claim ◽  
Binomial Approximation ◽  
The Individual

A functional approach is taken for the total claim amount distribution for the individual risk model. Various commonly used approximations for this distribution are considered, including the compound Poisson approximation, the compound binomial approximation, the compound negative binomial approximation and the normal approximation. These are shown to arise as zeroth order approximations in the functional set-up. By taking the derivative of the functional that maps the individual claim distributions onto the total claim amount distribution, new first order approximation formulae are obtained as refinements to the existing approximations. For particular choices of input, these new approximations are simple to calculate. Numerical examples, including the well-known Gerber portfolio, are considered. Corresponding approximations for stop-loss premiums are given.

scholarly journals RUIN PROBABILITY UNDER COMPOUND POISSON MODELS WITH RANDOM DISCOUNT FACTOR

2004 ◽  
Vol 18 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Kai W. Ng ◽  
Hailiang Yang ◽  
Lihong Zhang
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Poisson Model ◽  
Convergence Result ◽  
Discount Factor ◽  
Insurance Risk ◽  
Compound Poisson ◽  
Analysis Techniques ◽  
Surplus Process ◽  
Poisson Models

In this article, we consider a compound Poisson insurance risk model with a random discount factor. This model is also known as the compound filtered Poisson model. By using some stochastic analysis techniques, a convergence result for the discounted surplus process, an expression for the ruin probability, and the upper bounds for the ruin probability are obtained.

There Is No “I” in Team but There Is in Innovation: How Individual Attributes Impact Team Ideation and Selection Practices

2021 ◽  
Author(s):  
Aoran Peng ◽  
Sam Hunter ◽  
Scarlett R. Miller
Keyword(s):  
Positive Impact ◽  
Preliminary Evidence ◽  
Design Stage ◽  
Individual Risk ◽  
Team Composition ◽  
Concept Generation ◽  
Team Members ◽  
The Individual ◽  
The Impact

Abstract While teaming is a vital component of engineering, it is important to remember that there is no team without individuals and individual behavior can drive team outputs. One of these individual factors that may manifest itself at the team level is individual risk-taking attitudes, which can be impacted by personality and preferences for creativity. However, a gap exists in research on the impact of the team composition in these factors on creative outputs, as previous research has found that team composition plays a key role in team performance. The current work was developed to examine how the elevation and diversity of team personality and preferences for creativity impact the novelty and quality of ideas generated and selected by the team through a simulation study of 60,831 simulated teams. The results of this study show that the novelty and quality of ideas generated and selected can be predicted by the elevation and diversity of the simulated teams’ personality and PCS factors. In addition, it was found that the impact of the individual elevation and diversity factors can vary depending on the ideation trait (novelty and quality) and design stage (concept generation and selection). However, there was one variable that had a consistent positive impact on team behavior — the elevation of the Creative Confidence of the Simulated Team Members. These findings provide preliminary evidence on how individual attributes manifest themselves at the team level to impact team ideation and selection performances.

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.

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