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Tail conditional moment for generalized skew-elliptical distributions.

Esmat Jamshidi Eini1, Hamid Khaloozadeh1

  • 1Department of Systems and Control, K.N. Toosi University of Technology, Tehran, Iran.

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|June 16, 2022
PubMed
Summary

This study introduces an expanded tail conditional moment (TCM) measure for financial risk analysis, applicable to asymmetric data. The new method enhances understanding of risk behavior in loss distributions for better financial modeling.

Keywords:
Tail conditional expectationgeneralized skew-Elliptical distributionsmeasure of risktail conditional momentstail variance

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Area of Science:

  • Quantitative Finance
  • Financial Mathematics
  • Risk Management

Background:

  • Financial markets and insurance face evolving risks requiring robust benchmark structures.
  • Existing risk measures often rely on restrictive distributional assumptions.

Purpose of the Study:

  • To extend the tail conditional moment (TCM) measure beyond elliptical distributions.
  • To develop a flexible risk benchmark for asymmetric financial phenomena.
  • To introduce generalized tail conditional skewness (TCS) and kurtosis (TCK) measures.

Main Methods:

  • Developed a theorem to generalize the TCM measure for skew-elliptical distributions.
  • Derived analytical formulas for TCM, TCS, and TCK in generalized skew-elliptical settings.
  • Applied the proposed TCM measure to various generalized skew-elliptical distributions.

Main Results:

  • An analytical formula for TCM in skew-elliptical distributions was obtained.
  • Generalizations of TCS and TCK for loss distributions were derived.
  • The extended TCM measure was successfully applied to diverse distribution families.

Conclusions:

  • The proposed TCM measure effectively captures risk in asymmetric loss distributions.
  • The generalized TCS and TCK provide deeper insights into tail behavior.
  • The methodology offers a practical tool for portfolio risk assessment.