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Collective Risk Models with Dependence Uncertainty

SSRN Electronic Journal
2017
  • 4
    Citations
  • 1,454
    Usage
  • 1
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    4
    • Citation Indexes
      4
  • Usage
    1,454
    • Abstract Views
      1,270
    • Downloads
      184
  • Captures
    1
  • Ratings
    • Download Rank
      328,506

Article Description

We bring the recently developed framework of dependence uncertainty into collective risk models, one of the most classic models in actuarial science. We study the worst-case values of the Value-at-Risk (VaR) and the Expected Shortfall (ES) of the aggregate loss in collective risk models, under two settings of dependence uncertainty: (i) the counting random variable (claim frequency) and the individual losses (claim sizes) are independent, and the dependence of the individual losses is unknown; (ii) the dependence of the counting random variable and the individual losses is unknown. Analytical results for the worst-case values of ES are obtained. For the loss from a large portfolio of insurance policies, an asymptotic equivalence of VaR and ES is established. Our results can be used to provide approximations for VaR and ES in collective risk models with unknown dependence. Approximation errors are obtained in both cases.

Bibliographic Details

Haiyan Liu; Ruodu Wang

Elsevier BV

collective risk model; Value-at-Risk; Expected Shortfall; dependence uncertainty; asymptotic equivalence

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