Confidence Interval Estimation for Right-Tailed Deviation Risk Measures Under Heavy-Tailed Losses

The estimation of the price of an insurance risk is a very important actuarial problem. This price has to reflect the property of the distribution of the random variable describing the corresponding loss. If the loss variable has a heavy-tailed distribution (i.e. distribution with an infinite variance) then, the risk measure (as a measure of the risk premium) should be higher. For providing risk measures with heavy-tailed distributions, standard procedures from classical statistics (when the variance is finite) cannot be applied. In this paper we propose confidence interval estimation for the Wang's right-tailed deviation risk measure for heavy-tailed losses.