Tsallis Entropy for Loss Models and Survival Models Involving Truncated and Censored Random Variables

Area of Science:

• Actuarial Science
• Risk Management
• Information Theory

Background:

• Traditional actuarial models often struggle with truncated and censored data.
• Existing risk assessment methods may lack flexibility for complex insurance scenarios.
• Entropy measures offer a powerful tool for quantifying uncertainty in financial data.

Purpose of the Study:

• To develop an entropy-based risk assessment framework for actuarial models.
• To utilize the Tsallis entropy measure for analyzing losses with truncated and censored variables.
• To investigate the impact of partial insurance features on loss entropy.

Main Methods:

• Application of Tsallis entropy to actuarial models with truncated and censored random variables.
• Derivation of analytic expressions for per-payment and per-loss entropies.
• Computation of Tsallis entropy for specific loss distributions (exponential, Weibull, χ2, Gamma) under deductible and policy limits.
• Analysis of residual and past loss entropies and their relationships.

Main Results:

• Analytic expressions for per-payment and per-loss entropies were derived.
• The Tsallis entropy of losses was computed for various distributions under specific insurance conditions.
• Properties of residual and past loss entropies were studied in relation to deductibles and policy limits.
• Entropies for proportional hazard and reversed hazard models were derived.

Conclusions:

• The Tsallis entropy approach offers a more realistic and flexible method for actuarial risk assessment.
• This approach improves modeling accuracy for insurance data with truncation and censoring.
• The framework provides deeper insights into the impact of insurance features on risk evaluation.