Insurance risk analysis using tempered stable subordinator

Effective risk management in actuarial science requires precise modeling of claim severity, particularly for heavy-tailed distributions that capture extreme losses. This study investigates the applicability of the Tempered Stable Subordinator (TSS) distribution, a subclass of heavy-tailed distributions, as a robust tool for modeling claim severity in insurance portfolios. To evaluate its practical relevance, the TSS distribution's performance is compared to the widely utilized Gamma and Inverse Gaussian (IG) distributions, and their relative strengths in premium pricing are assessed using the Esscher transformation method. Premiums are calculated for each distribution, and their comparative advantages in the context of heavy-tailed risks are analyzed. Additionally, key risk measures such as Value at Risk (VaR) and Conditional Tail Expectation (CTE) are computed to evaluate the ability of each distribution to capture tail risk effectively. The findings reveal that the TSS distribution provides more flexibility and precision in modeling extreme insurance claims, positioning it as a valuable tool in actuarial risk management and premium pricing strategies.