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Second-order tail asymptotics of deflated risks
Insurance: Mathematics and Economics
Random deflation of risk models is an interesting topic for both theoretical and practical actuarial problems. In this paper, we investigate second-order tail asymptotics of the deflated risk X = RS under the assumptions of second-order regular variation on the survival functions of the risk R and the deflator S. Our findings are applied to derive second-order expansions of Value-at-Risk. Further we investigate the estimation of small tail probability for deflated risks and then discuss the asymptotics of the aggregated deflated risk.
Random deflation, Value-at-Risk, Risk aggregation, Second-order regular variation, Estimation of tail probability
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