預測是多數商業管理決策的基本要素，準確的預測可以幫助決策者做出正確的判斷，並且有助於提昇策略規劃的品質。保險是風險管理的方式之一，主要用於規避潛在的財務損失風險。在保險承保的範圍內，未來所有可能產生的損失，餘由當前被支付的保費來提供賠償。有鑑於此，保險公司有必要預估其現金流量，並做適當的資產負債管理，以避免將來喪失清償能力。本研究將具有白指數律重合性的預測方法應用於人身保險業保險給付之預測上，以解決發展條數較大時不能使用的限制。此外，為了提高預測的精確度，還另藉由傅立葉級數法來配過補償預測殘差。通過實例分析顯示，傳統灰色預測GM(1,l)模型之平均誤差百分比皆較殘差修正模型為高，由此可知，本研究所摔行之預測方法，無論是在模型精度或是預測的可信度土，均獲致了良好的結果。

Forecasting is an essential element of most business decision. Accurate prediction can help the policymaker make correct decision and promote the decision-making quality. Insurance is a form of risk management primarily used to hedge against the risk of potential financial loss. An insurance premium paid currently provides coverage for losses that might arise many years in the future. For that reason, the insurance company must forecast cash flows and perform asset-liability management to prevent insolvency. In this paper, the white exponential law coincidence property is adopted into the life insurance benefit payment forecasting method to solve the problem that the model cannot be used when the developing coefficient is large. In order to improve the forecasting precision, the Fourier series with suitably chosen values of parameters is used in the fitting of residual errors. Case studies show that the average error percentage of the conventional GM(1,1) model is higher than that of the residual modification model. The findings indicate that this method achieves reliable and precise results.