On automatic bias reduction for extreme expectile estimation.

Area of Science:

• Quantitative Finance
• Actuarial Science
• Statistical Modeling

Background:

• Expectiles are gaining traction as a coherent and elicitable risk measure in finance and actuarial science.
• Current extreme expectile estimators for heavy-tailed distributions suffer from bias, leading to poor performance in real-world samples.

Purpose of the Study:

• To develop bias-reduced extreme expectile estimators for heavy-tailed distributions.
• To improve the accuracy and finite-sample performance of risk measures in financial and actuarial applications.

Main Methods:

• Investigated asymptotic proportionality between extreme expectiles and quantiles.
• Utilized extrapolation formulas within a heavy-tailed context.
• Quantified and estimated bias in existing extreme expectile estimation methods.
• Developed and rigorously proved asymptotic properties of new bias-reduced estimators.

Main Results:

• Introduced novel classes of bias-reduced extreme expectile estimators.
• Demonstrated improved asymptotic and finite-sample properties compared to existing methods.
• Validated findings through simulation studies and real-world data from economics, insurance, and finance.

Conclusions:

• The proposed bias-reduced estimators offer a significant improvement for extreme expectile estimation in heavy-tailed distributions.
• These advancements enhance the reliability of risk management tools in actuarial and financial sectors.
• The study provides robust estimators suitable for practical applications with financial and insurance data.