Chain Ladder考量通貨膨脹對於IBNR估計之影響：ARIMA vs.局部多項式迴歸

Estimating Outstanding Claims Reserves with Inflation in the Chain Ladder：ARIMA vs. Local Polynomial Regression

賠款準備金是保險公司銷售短期保險商品所需提列的準備金，旨在確保保險公司未來能夠穩定經營。對精算人員而言，這是一項重要的工作。傳統的賠款準備金估計方法是Chain Ladder法，根據過去的理賠數據預測未來可能的理賠金額，估計尚未報告給保險公司的理賠準備金（IBNR）。然而，該方法僅考慮過去數據，未考慮通貨膨脹的影響。因此，本研究在Chain Ladder方法中引入通貨膨脹的考量，使用局部多項式迴歸來預測通貨膨脹率，並與Raeva &Pavlov (2022)的ARIMA模型進行比較。研究結果顯示使用局部多項式迴歸方法估計的IBNR平均相對誤差約為31%而優於ARIMA模型的33%；因此，使用局部多項式迴歸方法來估計IBNR在準確性似更具優勢。

Loss reserves are provisions set aside by insurance companies to ensure stable operations. Actuaries play a crucial role in estimating these reserves. The chain ladder method is commonly used, relying on past claims data to project future claim amounts, including incurred but not reported (IBNR) claims. However, this method ignores the impact of inflation on claims. This study incorporates inflation consideration using local polynomial regression, comparing it to the ARIMA model by Raeva & Pavlov (2022). Our study shows that the relative error of the local polynomial regression method for IBNR estimation is 31%, outperforming the 33% relative error of the ARIMA model and, hence, may improve the estimation accuracy of IBNR.