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.

本研究探討面臨顯著背景風險（諸如核保等風險）金融機構之投資策略，考量加入國外投資風險下，該金融機構如何決定最適動態資產配置策略，為充分反映市場風險、匯率風險及核保風險，本研究以隨機方程式描述資產價值及核保經驗之變動，並以假想之人壽保險公司作為討論對象，預估未來現金流量並建構公司財務資訊相關之隨機模型，給定最低資本限制下，於指定投資期限內達到全期淨值(盈餘)最佳效用值為目標。本文依照給定之背景風險建構隨機控制模型，利用動態規劃法求出最適資產配置。結果顯示最適投資組合將由三項要素組成：1.極小化盈餘變化之變異數之部位；2.類似於短期投資組合策略之避險部位；以及3.用以規避背景風險之避險部位。因為模型複雜性之限制，以逼近馬可夫理論之數值方法計算最適投資策略。 / This paper analyzes the optimal asset allocation for insurers and investors who are required to cope with significant background risks due to underwriting uncertainties and interest rate risks among a set of stochastic investment opportunities. In order to hedge properly the country risks due to local volatile financial market, the foreign investment opportunities are included in the optimal portfolio decision. In this study, detailed formulation using the projected cash flows of a hypothetical life insurance company and its related stochastic phenomena are constructed. The insurers are assumed to maximize the expected discounted utility of their surplus over the investment horizon under the minimal capital requirement. Our problem is formulated as a stochastic control framework. According to the optimal solution, the optimal portfolio can be characterized by three components: a hedging component minimizing the variance of the change in surplus, a hedging component familiar to myopic portfolio rule, and a risk hedging component against the background risks. Since the explicit solutions cannot be achieved due to model complexity, the Markov chain approximation methods are employed to obtain the optimal control solutions in our numerical illustration.

提撥原則是固定給付退休基金所必須特別重視的經營策略，提撥率為基金贊助者定期提撥於未來成員退休給付的準備金。過高的提撥率會造成基金管理上的財務壓力，退休金計劃採行相對提撥方式，將同時加重基金贊助者與基金成員的財務負擔，而過低的提撥率則會造成退休給付的準備金不足，將使退休基金未來面臨無力清償成員退休給付的困境，因此適當且長期穩定的提撥原則成為退休基金決策者的經營目標，而必須特別重視基金的財務風險管理。 本研究著重於探討如何數量化退休基金經營的穩定性與安全性，陳述隨機控制理論的觀點，應用動態規劃的發展結果，建立基金於離散時間的動態回饋控制模型，仔細探討並說明Haberman與Sung (1994)及Chang (1999a)所定義基金管理者的風險測度，使退休基金最主要的兩種經營風險，亦即提撥穩定性的風險（contribution rate risk）和財務清償的風險（solvency risk）能夠於基金財務規劃的期限內達到最小值，風險測度可提供決策者客觀衡量基金經營時的風險指標，表達有別於會計帳面之財務數字外有效的財務資訊。利用最適化的概念與給定參數及遞迴條件的限制下，計算基金於財務規劃期間內的最適提撥金額。 最後，我們以台灣公務人員退撫基金為研究對象進行數值分析，由實例分析的流程我們詳細探討最適化理論與實際財務評估的應用過程，且最適的結果可以提供退休基金決策者更詳盡且及時的財務資訊，輔助退休基金管理者於多期決策的擬定過程。 / Funding policy is the crucial management decision in the defined benefit pension schemes. The plan sponsor is required to calculate the contribution rate and accumulate in advance as he reserve for the future contingent retirement and ancillary obligations for the plan members. High contribution results an accelerating financial burden for the plan sponsor, while low contribution might endanger the financial solvency of the plan. The appropriate and stable contributions become the goal of the plan manager in setting up his funding policy. Hence financial risk management in attaining the goal is especially vital to be examined. The study emphasizes on quantifying the mismanage risks in pension valuation. The stability and solvency issues are included in our financial risk management. Stochastic control is also reviewed and the methodology of the dynamic programming is explored. The performance measure proposed in Haberman and Sung (1994) and Chang (1999a) are employed to scrutinize the contribution rate risk and solvency risk. The risk measurement can provide extra information in disclosing the risk index for the plan sponsor. The results gain operative information besides the traditional accounting reporting. The optimal contribution based on managerial consideration can be implemented through dynamic mechanisms under the given demographic and economic parameters and the plan recursive constraints. Finally, Taiwan public employees retirement system (Tai-PERS) is illustrated to investigate the optimal results and funding levels through the proposed model. The optimal results can response the updated financial information and assist the plan manager in policy making under the multi-frameworks.

本文於確定提撥退休金制度下，探討基金經理人如何決定最適資產策略規避薪資所得及通貨膨脹之不確定風險，求得期末財富效用期望值極大化。本研究首先擴展Battocchio與Menoncin (2004)所建構之資產模型，我們不僅探討來自市場之風險，同時考量薪資所得、通貨膨脹與費用率之不確定性，研究其對最適資產配置行為的影響，建構隨機控制模型，以動態規劃方法求解Hamiltonian方程式，研究結果顯示，我們可利用五項共同基金分離定理來描述投資人之最適投資決策：短期市場基金、狀態變數避險基金、薪資所得避險基金、通貨膨脹避險基金與現金部位。數值結果顯示，股票持有部位中通貨膨脹避險基金佔有最大的成份，債券持有部位中通貨膨脹避險基金與狀態變數避險基金佔有最大的成份。 關鍵字：確定提撥、薪資的不確定性、通貨膨脹、隨機控制、動態規劃 / In this study, we investigate the portfolio selection problem in order to hedge the labor income and inflation uncertainties for defined contribution (DC) pension schemes. First, we extend the previous work of Battocchio and Menoncin (2004) that allowed the state variables (i.e., the risks from the financial market) and a set of stochastic processes to describe the inflation, labor income and expense uncertainties. A five-fund separation theorem is derived to characterize the optimal investment strategy for DC pension plans to hedge the labor income and the inflation risks. Second, by solving the Hamiltonian equation in the three-asset framework, we show that the optimal portfolio consists of five components: the myopic market portfolio, the hedge portfolio for the state variables, the hedge portfolio for the inflation risk, the hedge portfolio for the labor income uncertainty and the riskless asset. Then we explicitly solve the optimal portfolio problem. Finally, the numerical results indicate that the inflation hedge portfolio comprises the overwhelming proportion of stock holdings in the optimal portfolios. In addition, the inflation hedge portfolio and the state variable hedge portfolio constitute the overwhelming proportions of bond holdings. Keywords: defined contribution; salary uncertainty; inflation; stochastic control; dynamic programming.