本文延續Huang(2004, 2008)的研究，將單期與多期挹注資金的資產負債管理議題專化於DC確定提撥退休金制度上，其研究將問題化成二次函數，以一般化最小平方法(Generalized least square, GLS)求出具有唯一解特性的決策變數，利用的軟體求解速度相當快，能有效率地一次找出多項資產配置比例。 本研究引入三種投資模型及其薪資模型，分別是Wilkie(1995)模型、MacDonald and Cairns(2007)模型、Huang and Cairns(2006)及Li(2009)，以蒙地卡羅模型模擬出各投資標的年報酬率與薪資水準，並利用這些預期的模擬值在負債目標控制為隨機成長或固定比例成長下，找出最適投資比例、每期挹注的額度與提撥比例。 最適配置為了解決下方風險(downside risk)問題，在允許限定風險容忍度下去最大化投資績效，本研究將目標函數加入衡量報酬項，依據員工希望的報酬，討論此項權重如何最適。亦加入交易成本項以反映實務情況，此投資總交易成本為權重的函數，於足夠支付交易成本的前提下找出權重最小值。 / In this study, the simulation of the return for each investment and wage pattern is via introduction of three investment model and their wage model, namely, Wilkie (1995) model, MacDonald and Cairns (2007) model, Huang and Cairns (2006) model and Li (2009), by using Monte Carlo simulation. The optimal contribution rate of investments, the amount of injection of each period, and income replacement ratio are determined when simulation is targeted in the balance control for the random growth or growth under a fixed rate of liabilities. The asset-liability management of single-period and multi-period injection of funds is specialized in the Defined contribution plan (DC), which is the extension of Huang’s (2004, 2008) study. Huang’s research transforming his argument into a quadratic function to generalized least squares method (GLS) having a unique solution to derive the decision-making variables. This method can efficiently find a set of allocation by software at a fairly rapid speed. The optimal allocation is to maximize investment performance subject to a limited risk had to tolerance for deal with downside risk. This study ameliorates the objective function by adding a constant term, which does not affect the investment decision-making variable. This new generalized least squares method use a constant represented as a weight, which is based on the desire asset of the employee. This study also takes transaction costs into consideration to reflect the practical situation. The total transaction costs are the function of the weight introduced into the new objective function. The minimum of weight can be reached when the goal is set to be sufficient to cover the transaction costs

本文主要在探討確定提撥退休金計劃下，投資決策對所得替代率之影響，以提供員工退休規劃及政府政策擬定之參考。首先，我們建構退休金累積模型及所得替代率模型，其中所得替代率之計算是以含通貨膨脹率因子的年金方式給付退休金。然後，將影響退休金累積模型的精算因子：累積期間的投資報酬率，依據過去的月資料配適出其母體分配，以模擬員工未來退休時，使用年金方式給付退休金的所得替代率。本文進一步，提供員工在不同投資報酬下應相對提撥多少百分比，以達到適當的所得替代率水準的參考標準，以滿足員工未來退休時的生活所需。我們以民國87年「勞工退休金條例草案」及台灣投資市場的實証資料進行研究，本研究結果如右：當僱主提撥6%月薪資時，(一)若員工可選擇投資標的，女性、男性員工所得替代率分均值分別介於48%~70%、52%~75%，而且選擇高度風險基金之所得替代率平均值皆較低度風險基金高出45 %，但為了使所得替代率小於60%的機率低於10%，女性、男性員工選擇高度風險基金需較低度風險基金分別多提撥3 %、2 %。(二)若退休基金由勞委會統籌管理，以過去實証平均報酬率8%，計算女性、男性員工所得替代率分別為50%、54%，但為達到60%所得替代率，女性、男性員工需分別相對提撥2%、1%。(三)比較「員工可選擇投資標的」與「勞委會統籌分配管理」兩種退休基金管理方式，若員工可選擇投資標的亦有最低保証收益，結果發現員工可選擇投資標的之投資績效及所得替代率皆優於勞委會統籌分配管理。 / The thesis investigates the impacts of the employee’s investment decision making on income replacement rate for defined contribution plan. We first construct the pension accumulation model to compute the final retirement benefit under defined contribution plan. Furthermore, the empirical data of the investment returns from mutual fund market and that from Labor Insurance Bureau are utilized to simulate the possible investment returns distribution for employee before retirement. The replacement rate is then calculated by assuming the employee will use his/her final retirement benefit to buy a single premium annuity with inflation index adjustment from the insurance company. Finally, based on simulation results from different scenarios, we suggest a relative employee contribution rate in order for employee to reach his/her objective replacement rate under different risk aversion levels. Our results show: 1. If the employee can make investment decision by investing in the mutual fund market, in average, female employee can have 48~70% replacement rate, while male employee can have 52~75%. We also find the replacement rate for employee selecting the high-risk mutual fund is 45% higher than those for selecting the low-risk mutual fund. 2. If the employee can not make investment decision and Labor Insurance Bureau allocate the pension asset, female employee can have 50% replacement rate, while male employee can have 54%. 3. Comparing the above two alternatives under the assumption that the employee has minimum guarantee return in both case, we find the first option can generate higher replacement rate for employee.

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.