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COLLECTIVE RISK MODELS WITH DEPENDENCE UNCERTAINTY

Published online by Cambridge University Press:  03 April 2017

Haiyan Liu  and
Ruodu Wang
Haiyan Liu
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L3G1, Canada E-Mail: h262liu@uwaterloo.ca
Ruodu Wang*
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L3G1, Canada
*
E-Mail: wang@uwaterloo.ca
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Abstract

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.

Keywords

Collective risk modelValue-at-RiskExpected Shortfalldependence uncertaintyasymptotic equivalence
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 2 , May 2017 , pp. 361 - 389
Copyright
Copyright © Astin Bulletin 2017 

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