Maximum Entropy Methods for Loss Data Analysis: Aggregation and Disaggregation Problems.

Area of Science:

• Quantitative Finance
• Actuarial Science
• Reliability Engineering

Background:

• Loss data analysis is critical in finance for risk capital computation and in insurance for risk premia determination.
• Reliability analysis requires understanding damage accumulation and event occurrence distributions.
• Often, aggregate risk data is available, but the statistical nature of contributing events is unknown.

Purpose of the Study:

• To illustrate the application of the maximum entropy method for computing loss distributions.
• To demonstrate how this method addresses challenges in loss data analysis, including measurement errors and interval data.
• To assess the dependence of loss distributions on empirical data.

Main Methods:

• Utilizing the maximum entropy method and its extensions for numerical computation of loss distributions.
• Applying these methods to handle situations with aggregate risk data and unknown contributing event statistics.
• Incorporating techniques to manage data with measurement errors and interval-based information.

Main Results:

• The maximum entropy method provides a robust framework for calculating loss distributions.
• The approach effectively handles complex scenarios, including aggregate data and noisy measurements.
• Demonstrated the ability to assess the sensitivity of loss distributions to the underlying empirical data.

Conclusions:

• The maximum entropy method is a powerful tool for loss data analysis in various quantitative fields.
• Its robustness and extensibility make it suitable for real-world data challenges, including measurement inaccuracies.
• This method enhances the accurate computation and understanding of loss distributions and associated risks.