Confidence intervals for a tail index estimator

Financial data (log-returns of exchange rates, stock indices, share prices) are often modeled by heavy-tailed distributions, i.e., distributions which admit the representation $$P(X > x) = L(x){x^{ - 1/a}}(a > 0)$$ (14.1) where the function L slowly varies: \(\mathop {\lim }\limits_{x \to \infty } L(xt)/L(x) = 1(\forall t > 0)\).