Kernel-type estimators for the distortion risk premiums of heavy-tailed distributions. (English) Zbl 1401.62203
Summary: A new kernel-type estimator for the distortion risk premiums of heavy-tailed losses is introduced. Using a least-squares approach, a bias-reduced version of this estimator is proposed. Under suitable assumptions, the asymptotic normality of the given estimators is established. A small simulation study, to illustrate the performance of our method, is carried out.
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62G32 | Statistics of extreme values; tail inference |
| 62G30 | Order statistics; empirical distribution functions |
| 91B30 | Risk theory, insurance (MSC2010) |
Keywords:
risk measure; bias reduction; Hill estimator; high quantile; tail index; second-order regular variation; extreme valueSoftware:
RReferences:
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