A COMPARATIVE STUDY OF IBNR CLAIM RESERVE ESTIMATION USING BENKTANDER, WALTER NEUHAUS, AND OPTIMAL CREDIBILITY LOSS RATIO APPROACHES

Abstract

Reinsurance plays a crucial role in risk transfer for insurance companies, particularly in managing large and volatile losses. One of the key challenges in reinsurance is the accurate estimation of Incurred But Not Reported (IBNR) claim reserves, especially for nonproportional assumed property business, which is characterized by high claim volatility and delayed reporting patterns. This study provides an empirical comparison of credibility-based reserving methods—namely the Benktander and Walter Neuhaus approaches—using reported claims and earned premium data from United States reinsurance companies for the period 2010–2019. Unlike most existing studies that focus on proportional or direct insurance portfolios, this research evaluates the performance of these methods in a nonproportional reinsurance context and benchmarks them against the Optimal Credibility Loss Ratio method, which minimizes Mean Squared Error (MSE). Claim reserves are estimated using run-off triangle techniques, loss development factors, and credibility weighting schemes, and the accuracy of each method is assessed through MSE ratios. The results show that the Benktander method produces reserve estimates that are consistently closer to the optimal benchmark, with an average MSE ratio of 1.0265, compared to 1.4184 for the Walter Neuhaus method. These findings indicate that the Benktander approach offers a more stable and statistically efficient reserve estimation for immature and volatile nonproportional reinsurance data. The study contributes to actuarial reserving literature by providing empirical evidence on the relative effectiveness of credibility-based methods and offering practical insights for actuaries in selecting appropriate IBNR reserving techniques under high uncertainty.