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.