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Common mixture in the individual risk model. (English) Zbl 1187.91094

Summary: We propose a dependence structure based on common mixture models to allow a possible correlation between risks in the individual risk model. This model can be applied in an insurance context or in a credit risk context where one or more factors have an impact on the experience of the whole portfolio.
We measure the global risk of a portfolio via the aggregate claim amount distribution. The evaluation of such a quantity can become cumbersome in cases of large portfolios. To overcome this problem, we use the compound Poisson approximation within the proposed common mixture model and then evaluate the quality of this approximation.
We also give numerical examples in which we examine the riskiness of portfolios under the correlation structure proposed in this paper and apply the compound Poisson approximation. Finally, we establish the link between the common mixture model proposed and the family of Archimedean copulas.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G40 Credit risk
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