Loss Development Factors and Triangle Analysis

Loss Development Triangles

Loss development triangles are the fundamental data structure for property and casualty reserve analysis. Each row represents an accident year (or policy year), and each column represents a development period (typically measured in months or years from the start of the accident year). The entries show cumulative paid or incurred losses at each development stage. As claims are reported, investigated, and settled, losses "develop" over time. The pattern of development from one period to the next forms the basis for projecting immature accident years to their ultimate values.

Age-to-Age Factors

Age-to-age factors (also called link ratios or loss development factors) measure the ratio of losses at successive development periods. The chain ladder method selects a set of factors (using volume-weighted averages, simple averages, or medians) and applies them sequentially to project each accident year to ultimate. The selection of appropriate factors requires actuarial judgment, considering trends in claims handling, legal environment changes, and mix of business shifts. Tail factors, which estimate development beyond the observed triangle, often have the greatest impact on ultimate loss estimates and represent a significant source of uncertainty.