On two dependent individual risk models

Cossette, Hélène; Gaillardetz, Patrice; Marceau, Étienne; Rioux, Jacques E.

doi:10.1016/s0167-6687(02)00094-x

Cited by 41 publications

(21 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This is a traditional individual risk model. Another version of model (4.4) can be found in Cossette, et al (2002). We illustrate the effects of dependence on the optimal retention in this model by setting n = 2 in the following example.…”

Section: Dependent Risks Associated With a Multivariate Bernoulli Dismentioning

confidence: 99%

Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures

Cai¹,

Tan²

2007

ASTIN Bull.

175

120

View full text Add to dashboard Cite

We propose practical solutions for the determination of optimal retentions in a stop-loss reinsurance. We develop two new optimization criteria for deriving the optimal retentions by, respectively, minimizing the value-at-risk (VaR) and the conditional tail expectation (CTE) of the total risks of an insurer. We establish necessary and sufficient conditions for the existence of the optimal retentions for two risk models: individual risk model and collective risk model. The resulting optimal solution of our optimization criterion has several important characteristics: (i) the optimal retention has a very simple analytic form; (ii) the optimal retention depends only on the assumed loss distribution and the reinsurer's safety loading factor; (iii) the CTE criterion is more applicable than the VaR criterion in the sense that the optimal condition for the former is less restrictive than the latter; (iv) if optimal solutions exist, then both VaR-and CTE-based optimization criteria yield the same optimal retentions. In terms of applications, we extend the results to the individual risk models with dependent risks and use multivariate phase type distribution, multivariate Pareto distribution and multivariate Bernoulli distribution to illustrate the effect of dependence on optimal retentions. We also use the compound Poisson distribution and the compound negative binomial distribution to illustrate the optimal retentions in a collective risk model.

show abstract

Section: Dependent Risks Associated With a Multivariate Bernoulli Dismentioning

confidence: 99%

Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures

Cai¹,

Tan²

2007

ASTIN Bull.

175

120

View full text Add to dashboard Cite

show abstract

“…For purposes of developing these asymptotic properties, we focus on the credibility premium formula in (6) where this premium is the weighted sum of the observed sample means of the individual and the rest of the individuals. Similar interesting observations can be made if one focus on the credibility premium formula in (7).…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

“…Several general-izations and alternative models of dependence have since followed including, Goovaerts (1996, 1997) and Müller (1997), addressing their impact on stop-loss premiums. Other models have included the works of Genest, et al (1999) and Cossette, et al (2002) where claim dependence have been addressed in the framework of individual risk models. Furthermore, using the notion of a stochastic order, the recent papers by Denuit (2002, 2003) provide excellent discussion of dependencies in claim frequency for credibility models.…”

Section: Introductionmentioning

confidence: 99%

Claim dependence with common effects in credibility models

Yeo

Valdez

2006

Insurance: Mathematics and Economics

View full text Add to dashboard Cite

“…Analyzing the distribution of S is essential in finance and insurance for quantifying the risk of loss. In this regard, there are studies that have analyzed the stochastic behaviour of the sum of dependent risks and the way in which the dependency between these marginal risks may affect the total risk of loss (see, Denuit et al, 1999;Kaas et al, 2000;Cossette et al, 2002;Bolancé et al, 2008b). The aim of this paper is to analyze the test proposed by Kojadinovic et al (2011) that allows to test whether or not our data have been generated by an extreme value copula.…”

Section: Introductionmentioning

confidence: 99%

Testing Extreme Value Copulas to Estimate the Quantile

2013

View full text Add to dashboard Cite

We generalize the test proposed by Kojadinovic, Segers and Yan which is used for testing whether the data belongs to the family of extreme value copulas. We prove that the generalized test can be applied whatever the alternative hypothesis. We also study the effect of using different extreme value copulas in the context of risk estimation. To measure the risk we use a quantile. Our results have been motivated by a bivariate sample of losses from a real database of auto insurance claims.MSC: MSC62-07 MSC62F05.

show abstract

On two dependent individual risk models

Cited by 41 publications

References 18 publications

Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures

Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures

Claim dependence with common effects in credibility models

Testing Extreme Value Copulas to Estimate the Quantile

Contact Info

Product

Resources

About