不同評估績效的長短顯著地影響基金的經營策略，相較於強調穩健經營的退休基金而言，此因素是否亦影響退休基金的運作，本研究嘗試應用隨機控制理論，將投資績效的時間因素納入決策考量，以隨機微分方程式描述退休基金資產和應計負債的動態隨機行為，以多期基金規劃的觀點，探討時間因素與最適策略之關連性。本研究應用Brennan、Schwartz與Lagnado（1997）的結果至負債導向的退休基金管理，建構多期資產負債管理模型，退休基金持有資產將分類為風險性的股票投資組合、長期債券和短期票券，並考量投資標的短期利率與長期利率之隨機性質，將基金提撥與資產配置視為可調節因子，給定風險評估測度，於不設定投資限制下計算各期最適投資比例及基金提撥；本研究並以私人退休金個案進行模擬分析，結果顯示此基金未來10年之最適提撥率介於4.2﹪與5.1﹪，就不同評估期限而言，5年評估期之提撥率於初期高於10年評估期，基金比率η=0.75之提撥率低於η=1；5年評估期之基金交易行為較10年期明顯劇烈，基金比率較低時，其交易變化程度較小，不同評估年限與基金比率將同時影響退休基金之最適提撥與投資策略。 / Distinct time horizons in measuring investment perfomance significantly influence the financial planning for the money managers. In this study, we explore this issue concerning the pension fund management that has focused on the asset and liability management to meet its future obligations. A stochastic control model is formulated in a continuous-time framework to obtain the closed form solution for optimal strategy. The time variation in expected returns introduced in Brennan, Schwartz and Lagnado（1997）is adopted in obtaining the optimal strategy using plausible future plan’s normal costs and accrued liabilities under distinct time horizons. Based on the proposed performance measurement, the optimal funding schedule and portfolio selections are determined dynamically without trading restrictions. A private pension scheme is selected and analyzed for numerical illustration. It shows that the optimal contribution rates are between 4.2﹪and 5.1﹪for this specific case. Comparing the funding schedules for distinct time horizons, we find that the contribution rates under 5-year period are higher than those under 10-year period in the beginning. The contribution rates given funding ratio at 75﹪are lower than those given at 100﹪. While the optimal trading behaviors of the pension fund managers for 5-year period are significant volatile than those for 10-year period. Their optimal trading behaviors have exhibited a reduced volatility under the lower funding ratios. The case study indicates that the distinct time horizon and the funding ratio play crucial roles in decision-making process for pension fund management.

本研究針對退休基金管理的兩項重要議題：提撥政策與資產配置作最適規劃之探討。由於傳統退休基金的評價僅考慮單一期間的離散時間模型，不若多期規劃的效率性，因此，本研究考量連續時間下，利用控制理論觀點，將提撥金額與資產配置視為可調節的因子，以風險最小化為最適定義，提供基金多期管理的有效方法。 首先，為充分反映退休基金管理時所面臨的不確定因素，本研究假設資產價值服從幾何布朗運動，並且經由隨機微分方程式描述退休基金所累積資產與應計負債的動態隨機性質。其次，考量基金管理所面臨的提撥風險與清償風險，給定能夠量化這些風險的評估測度，藉以監督退休基金於管理期間的經營績效，並且利用Bellman方程式求出最適的基金提撥與資產配置策略。 最後以勞動基準法規範下的企業退休金計劃為實證對象，透過動態模擬估計模型中之參數，並且利用數值方法求出所需的函數值，將控制理論與情境模擬連結，藉以檢視現行固定給付退休基金之最適策略。由實證結果可知，透過本研究的方法的確可以有效管理基金同時符合財務清償能力的要求。利用動態規劃所得的最適策略與給定的風險評估函數相關，因此，基金決策者可以依據基金的特性給定適當的風險評估函數，依照不同的投資期限擬定合適的基金策略。 / This study explores two critical issues in pension fund management: funding policy and asset allocation. The traditional valuation of pension fund is restricted in one-period setting under discrete-time framework, and it is not efficient comparing to the continuous-time models. Therefore, in this study, control theory is employed to obtain the optimal strategy based on a specific plan dynamics. Employer's contributions and investment proportions are treated as the controllers in our model. Optimal solutions are obtained by minimizing the given risk performance in monitoring the multi-period fund management. First, the stochastic differential equations are constructed to describe the dynamics of the funding levels and the accrued liabilities. Geometric Brownian motions are used to model the assets held by the fund manager. Secondly, a stochastic control model with given risk measurement is formulated in a continuous-time framework to investigate the optimal decisions. In our approach, the plan's normal costs and accrued liabilities are simulated through plausible scenarios while the optimal contribution and asset allocation are solved through Bellman equation. At last, a specific pension scheme under the regulation of the Taiwan labor standards law is studied for numerical illustrations. A monitoring mechanism linking plausible scenarios and the closed-form solutions are employed to scrutinize the funding policy and asset allocation. The optimal strategies are estimated through dynamic programming under realistic workforce scenario. According to the result, it shows that the methodology in this study can assist the fund manager in obtaining the plan's financial soundness. Meanwhile, the optimal strategy can fully incorporate the given risk measurement. Hence, the policy maker can input certain managerial considerations into the performance measure to investigate the stability and solvency issues.