Estimating the Conditional Tail Expectation in the Case of Heavy-Tailed Losses

Table 1

Point estimates ${\widetilde{\mathrm{CTE}\hspace{0.17em}}}_n(t)$ and 95% confidence intervals for ${\mathrm{CTE}\hspace{0.17em}}_F(t)$ when $\gamma =2/3$.

$t=0.75$	$\text{CT}{\text{E}}_F(t)=7.005$
$n$	$k^{*}$	${\widetilde{\mathrm{CTE}\hspace{0.17em}}}_n(t)$	error	rmse	lower	upper	cover	length
$1000$	$054$	$6.876$	$0.045$	$0.303$	$6.356$	$7.397$	$0.839$	$1.041$
$2000$	$100$	$6.831$	$0.025$	$0.231$	$6.463$	$7.199$	$0.882$	$0.736$
$5000$	$219$	$7.119$	$0.016$	$0.194$	$6.881$	$7.357$	$0.895$	$0.476$
$t=0.90$	$\text{CT}{\text{E}}_F(t)=12.533$
$n$	$k^{*}$	${\widetilde{\mathrm{CTE}\hspace{0.17em}}}_n(t)$	error	rmse	lower	upper	cover	length
$1000$	$054$	$12.753$	$0.017$	$0.534$	$12.241$	$13.269$	$0.847$	$1.028$
$2000$	$100$	$12.487$	$0.003$	$0.294$	$12.137$	$12.838$	$0.841$	$0.701$
$5000$	$219$	$12.461$	$0.005$	$0.236$	$12.246$	$12.676$	$0.887$	$0.430$