scholarly journals Aggregate claim models with one-way and two-way dependence among individual claims

2018 ◽  
Vol 6 (3) ◽  
Author(s):  
Xueyuan Wu ◽  
Kam Chuen Yuen ◽  
Pengcheng Zhang
Keyword(s):  
Aggregate Claim

COMPARISON OF APPROXIMATIONS FOR COMPOUND POISSON PROCESSES

2015 ◽  
Vol 45 (3) ◽  
pp. 601-637 ◽  
Author(s):  
Raffaello Seri ◽  
Christine Choirat
Keyword(s):  
Random Variable ◽  
Cumulative Distribution ◽  
Claim Amount ◽  
Approximation Methods ◽  
Total Claim Amount ◽  
Aggregate Claim ◽  
Time Period ◽  
Total Claim ◽  
The Difference ◽  
Object Of Study

AbstractIn this paper, we compare the error in several approximation methods for the cumulative aggregate claim distribution customarily used in the collective model of insurance theory. In this model, it is usually supposed that a portfolio is at risk for a time period of length t. The occurrences of the claims are governed by a Poisson process of intensity μ so that the number of claims in [0,t] is a Poisson random variable with parameter λ = μ t. Each single claim is an independent replication of the random variable X, representing the claim severity. The aggregate claim or total claim amount process in [0,t] is represented by the random sum of N independent replications of X, whose cumulative distribution function (cdf) is the object of study. Due to its computational complexity, several approximation methods for this cdf have been proposed. In this paper, we consider 15 approximations put forward in the literature that only use information on the lower order moments of the involved distributions. For each approximation, we consider the difference between the true distribution and the approximating one and we propose to use expansions of this difference related to Edgeworth series to measure their accuracy as λ = μ t diverges to infinity. Using these expansions, several statements concerning the quality of approximations for the distribution of the aggregate claim process can find theoretical support. Other statements can be disproved on the same grounds. Finally, we investigate numerically the accuracy of the proposed formulas.

ON HETEROGENEITY IN THE INDIVIDUAL MODEL WITH BOTH DEPENDENT CLAIM OCCURRENCES AND SEVERITIES

2018 ◽  
Vol 48 (02) ◽  
pp. 817-839 ◽  
Author(s):  
Yiying Zhang ◽  
Xiaohu Li ◽  
Ka Chun Cheung
Keyword(s):  
Claim Amount ◽  
Common Belief ◽  
Individual Model ◽  
Numerical Examples ◽  
Scale Parameters ◽  
Aggregate Claim ◽  
Left Tail ◽  
Insurance Portfolio ◽  
The Individual ◽  
Arrangement Increasing

AbstractIt is a common belief for actuaries that the heterogeneity of claim severities in a given insurance portfolio tends to increase its dangerousness, which results in requiring more capital for covering claims. This paper aims to investigate the effects of orderings and heterogeneity among scale parameters on the aggregate claim amount when both claim occurrence probabilities and claim severities are dependent. Under the assumption that the claim occurrence probabilities are left tail weakly stochastic arrangement increasing, the actuaries' belief is examined from two directions, i.e., claim severities are comonotonic or right tail weakly stochastic arrangement increasing. Numerical examples are provided to validate these theoretical findings. An application in assets allocation is addressed as well.

scholarly journals Asymptotic Dependence of Reinsurance Aggregate Claim Amounts

2003 ◽  
Vol 33 (2) ◽  
pp. 239-263
Author(s):  
Ana J. Mata
Keyword(s):  
Asymptotic Behaviour ◽  
Joint Distribution ◽  
Asymptotic Dependence ◽  
Marginal Distributions ◽  
Retention Level ◽  
Aggregate Claim

In this paper we study the asymptotic behaviour of the joint distribution of reinsurance aggregate claim amounts for large values of the retention level under various dependence assumptions. We prove that, under certain dependence assumptions, for large values of the retention level the ratio between the joint distribution of the aggregate losses and the product of the marginal distributions converges to a constant value that only depends on the frequency parameters.

scholarly journals Third cumulant for multivariate aggregate claim models

2017 ◽  
Vol 2018 (2) ◽  
pp. 109-128 ◽  
Author(s):  
Nicola Loperfido ◽  
Stepan Mazur ◽  
Krzysztof Podgórski
Keyword(s):  
Aggregate Claim

Modelling Income Protection Claim Termination Rates by Cause of Sickness I: Recoveries

2009 ◽  
Vol 4 (2) ◽  
pp. 199-239 ◽  
Author(s):  
S. Y. Ling ◽  
H. R. Waters ◽  
A. D. Wilkie
Keyword(s):  
Linear Models ◽  
Cox Model ◽  
Swine Flu ◽  
Insurance Claims ◽  
Generalised Linear Models ◽  
The Past ◽  
Aggregate Claim ◽  
Over Time

ABSTRACTIn this paper we present methods and results for the estimation and modelling of the recovery intensity for Income Protection (IP) insurance claims, allowing for different causes of claim. We use UK data supplied by the Continuous Mortality Investigation relating to claims paid in the years 1975 to 2002, inclusive. Each claim is classified by one of 70 possible causes according to ICD8.We group causes where appropriate, and then use the Cox model and generalised linear models to model the recovery intensity.In two subsequent papers we complete our modelling of IP claim termination rates by discussing the modelling of the mortality of IP claimants.There are two main reasons why it is useful to incorporate cause of sickness in the modelling of IP claim terminations:(i) The cause of sickness will be known to the insurer for a claim in the course of payment. A reserve can be set more accurately for such a claim if a model of the termination rates appropriate for this cause is available.(ii) Different causes of claim will become more or less significant over time. For example, tuberculosis may have been an important cause of sickness in the past, but is likely to be far less significant now; the swine flu pandemic starting in 2009 is likely to have a significant effect on observed aggregate claim termination rates, skewing them towards higher rates at shorter durations. Information about trends in morbidity, together with a model of termination rates by cause of claim, allows future aggregate claim termination rates to be predicted more accurately, reserves to be set at more appropriate levels and policies to be priced more accurately.One of the covariates included in our models for recovery intensities is Calendar Year. Aggregate recovery intensities have been decreasing over the period considered, 1975 to 2002, and this is generally reflected in the models for recovery intensities by cause of sickness. However, when these intensities are projected for years beyond 2002, the results are not always plausible.

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