Estimation of premiums for heavy-tailed loss

Pricing of an Insurance product is a necessary but not easy issue for Insurance company. To meet the no-arbitrary pricing model in asset pricing theory, Wang (1995) proposed a recent premium principle named proportional hazards transform. Amount of premiums under this principle can be estimated by parametric, nonparametric and semi-parametric methods. We compare different estimators for heavy-tailed losses within a limited sample size. In particular, we investigate theasymptotic normality of extremes estimators. The detailed simulation study in this thesis clearly demonstrates the excellent performance of extreme estimators.