A Comparative Study of Fuzzy Chain Ladder and Fuzzy Bornhuetter-Ferguson Methods for Claims Reserving - Mujiati Dwi Kartikasari (Department of Statistics ITS, 2026)
Accurate estimation of claim reserves is critical for the solvency of non-life insurance companies. Classical deterministic methods, such as Chain Ladder (CL) and Bornhuetter-Ferguson (BF), often fail to capture the inherent vagueness in actuarial judgments regarding development patterns and prior information. Fuzzy Set Theory, particularly through Triangular Fuzzy Numbers (TFNs), offers a formal framework to model this imprecision. This study conducts an empirical comparative analysis of two fuzzy reserving methods: the Fuzzy Chain Ladder (FCL) and the Fuzzy Bornhuetter-Ferguson (FBF). The FCL method fuzzifies the development factors, while the FBF method extends fuzzification to both the development pattern and the prior estimate of ultimate losses. Both methods are applied to a real-world liability insurance claims dataset from an Indonesian company, structured into a run-off triangle. The performance is evaluated by comparing the central reserve estimates, the total model uncertainty, and the asymmetry of the fuzzy output intervals. The results indicate that the FCL method produces a more conservative and volatile central reserve, approximately 12.3% higher than the FBF estimate under a risk-neutral assumption. More importantly, the FBF method demonstrates superior stability, with a total uncertainty measure about 14.7% lower than FCL, and exhibits an asymmetric uncertainty structure in which the right spread is consistently narrower, making its defuzzified reserve less sensitive to the actuary's risk attitude. The study concludes that the FCL method is suitable as a transparent, data-driven benchmark, whereas the FBF method is recommended for generating more robust and risk-sensitive forecasts when credible prior information is available.