Estimating copula-based extension of tail value-at-risk and its application in insurance claim

Dependent Tail Value-at-Risk, abbreviated as DTVaR, is a copula-based extension of Tail Value-at-Risk (TVaR). This risk measure is an expectation of a target loss once the loss and its associated loss are above their respective quantiles but bounded above by their respective larger quantiles. In this paper, we propose nonparametric estimators for DTVaR and establish their property of consistency. Moreover, we also propose the variability measure around this expected value truncated by the quantiles, called the Dependent Conditional Tail Variance (DCTV). We use this measure for constructing confidence intervals of the DTVaR. Both parametric and nonparametric approaches for DTVaR estimations are explored. Furthermore, we assess the performance of DTVaR estimations using a proposed backtest based on the DCTV. As for the numerical study, we take an application in the insurance claim amount.