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Insurance risk analysis using tempered stable subordinator.

Tuğba Aktaş Aslan1, Başak Bulut Karageyik2

  • 1Department of Actuarial Sciences, Faculty of Economics and Administrative Sciences, Kirikkale University, Kirikkale, Türkiye.

Journal of Applied Statistics
|February 6, 2026
PubMed
Summary

The Tempered Stable Subordinator (TSS) distribution offers superior flexibility for modeling extreme insurance claims compared to Gamma and Inverse Gaussian distributions. This enhances actuarial risk management and premium pricing for heavy-tailed risks.

Keywords:
62P0597M30Esscher transformTempered stable subordinator (TSS)heavy-tailed distrbiutionsinsurancerisk measures

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Area of Science:

  • Actuarial science
  • Quantitative finance
  • Risk management

Background:

  • Effective risk management necessitates precise modeling of claim severity, especially for heavy-tailed distributions capturing extreme losses.
  • Heavy-tailed distributions are crucial for accurately assessing insurance portfolio risks.

Purpose of the Study:

  • To investigate the applicability of the Tempered Stable Subordinator (TSS) distribution for modeling insurance claim severity.
  • To compare the performance of the TSS distribution against Gamma and Inverse Gaussian (IG) distributions.
  • To assess the relative strengths of these distributions in premium pricing and risk measure calculation.

Main Methods:

  • Comparative analysis of TSS, Gamma, and IG distributions for claim severity modeling.
  • Application of the Esscher transformation method for premium pricing.
  • Calculation of key risk measures: Value at Risk (VaR) and Conditional Tail Expectation (CTE).

Main Results:

  • The TSS distribution demonstrated greater flexibility and precision in modeling extreme insurance claims.
  • Comparative analysis revealed advantages of TSS in capturing tail risk effectively.
  • Premium pricing and risk assessment showed TSS as a robust alternative.

Conclusions:

  • The TSS distribution is a valuable tool for actuarial risk management and premium pricing.
  • Its ability to model heavy-tailed distributions enhances the precision of risk assessments.
  • Findings support the adoption of TSS for managing extreme insurance claim scenarios.