Transition Matrix Theory and Individual Claim Loss Development

Motivation: Individual claim development is important for creating the average severity distributions that underlie most increased limits, and reinsurance pricing analyses, but most current methods do not adequately represent the true process.

Method: Transition Matrix Theory is applied to a large database of reinsurance data. The data is processed to isolate GL data, and the Transition Matrix process is described in detail.

Results: Individual claim size development is characterized as a distributional process. The effect of this distributional process on pricing parameters is contrasted with traditional methods.

Conclusions: Individual Claim Size development is a distributional process, and can be measured and introduced into procedures for calculating average severity distributions. A simple five parameter formula can model this process. The Transition Matrix process may overstate the distribution of the ultimate distribution, but this can be measured and corrected. Pricing parameters are affected by this process and its effect should be factored in when possible.

Keywords: Transition Matrix, Average Severity, Individual Claim Loss Development, Distributional Loss Development