Second-order tail asymptotics of deflated risks

•Second-order tail asymptotics of deflated risks are investigated for three MDA cases.•Several examples illustrate the increased accuracy achieved using our results.•We apply our results to VaR, tail probability and aggregated risk.•Second-order properties of common insurance risks are derived.

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.