Bias correction for estimated distortion risk measure using the bootstrap

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The bias of the empirical estimate of a given risk measure has recently been of interest in the risk management literature. In particular, Kim and Hardy (2007) showed that the bias can be corrected for the Conditional Tail Expectation (CTE, a.k.a. Tail-VaR or Expected Shortfall) using the bootstrap. This article extends their result to the distortion risk measure (DRM) class where the CTE is a special case. In particular, through the exact bootstrap, it is analytically proved that the bias of the empirical estimate of DRM with concave distortion function is negative and can be corrected on the bootstrap, using the fact that the bootstrapped loss is majorized by the original loss vector. Since the class of DRM is a subset of the L-estimator class, the result provides a sufficient condition for the bootstrap bias correction for L-estimators. Numerical examples are presented to show the effectiveness of the bootstrap bias correction. Later a practical guideline to choose the estimate with a lower mean squared error is also proposed based on the analytic form of the double bootstrapped estimate, which can be useful in estimating risk measures where the bias is non-cumulative across loss portfolio.

Original languageEnglish
Pages (from-to)198-205
Number of pages8
JournalInsurance: Mathematics and Economics
Issue number2
Publication statusPublished - 2010 Oct

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Bias correction for estimated distortion risk measure using the bootstrap'. Together they form a unique fingerprint.

Cite this