Collective Risk Models with Dependence Uncertainty

ASTIN Bulletin, Forthcoming

29 Pages Posted: 26 Mar 2016 Last revised: 27 Feb 2017

See all articles by Haiyan Liu

Haiyan Liu

Michigan State University - Department of Mathematics

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: February 25, 2017

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 model, Value-at-Risk, Expected Shortfall, dependence uncertainty, asymptotic equivalence

Suggested Citation

Liu, Haiyan and Wang, Ruodu, Collective Risk Models with Dependence Uncertainty (February 25, 2017). ASTIN Bulletin, Forthcoming , Available at SSRN: https://ssrn.com/abstract=2754135 or http://dx.doi.org/10.2139/ssrn.2754135

Haiyan Liu

Michigan State University - Department of Mathematics ( email )

619 Red Cedar Road
East Lansing, MI 48824
United States

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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