[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Claim Count Triangle** ## Definition ==Claim Count Triangle== is a development triangle displaying the number of claims (rather than dollar amounts) by accident year and development age, used to analyze claim frequency patterns and development. ## Structure ``` Example Claim Count Triangle: Development Age (months) AY 12 24 36 48 60 2020 450 520 545 552 555 2021 475 550 580 590 2022 500 575 610 2023 525 605 2024 550 ``` ## Uses ### Frequency Analysis - Track claim reporting patterns - Identify changes in claim frequency - Support frequency-severity methods - Validate loss triangles ### Diagnostic Tool ``` Closed Claim Counts: - Monitor settlement rates - Assess claims department efficiency - Identify changes in closing patterns Reported Claim Counts: - Analyze reporting lags - Detect operational changes - Project ultimate claim counts ``` ### Combined with Loss Triangles ``` Average Severity = Loss Amount / Claim Count Can develop separately: - Frequency (claim counts) - Severity (average per claim) - Multiply for ultimate losses ``` ## Development Patterns ``` Count development factors typically: - Develop less than loss amounts - More stable over time - Lower tail factors - Mature faster Example: 12-24 count factor: 1.155 12-24 loss factor: 1.600 (Severity increasing as claims develop) ``` ## Related Concepts - [[Loss Development Triangle#Definition]] - [[Frequency-Severity Method#Definition]] - [[Frequency Analysis#Definition]] ## References - Friedland, Chapter 8