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.

在老人絕對數量與相對比率逐漸增加、產業結構改變、扶養意識與能力低落之今日，老年經濟安全的問題日益顯得重要。睽諸已開發國家之經驗概況，皆以「確保老年經濟安全」此一保障制度列為其主要施政內容，其中大多採行世界銀行之多層年金保障制度，利用重分配、儲蓄和保險三項不完全相容之功能搭配運用，並依國情、經濟狀況與人口結構等因素取得最適之平衡模式，達成各種社會與經濟的目標。 我國目前亦實施多層老年保障年金制度，回顧過去行之多年之公、勞保制度，不難發現其給付水準普遍有偏低之情況，僅能提供老年基本之生活保障。而規劃中之國民年金亦將採取「業務分立、內涵整合」原則之社會保險方式辦理，強制25歲至64歲之國民一律參加，而無法依照不同身份、類別設計符合個別需求，故不易以提高繳納保費來提升老年生活保障程度。再者，依過去公共年金計畫之經驗，常有超出意料之外使財政負擔日益加重，進而產生世代間負債之移轉，導致年金制度之推行影響其他市場之運作。在在都顯示第二層職業年金之不可或缺性，因此惟有公、私年金之互相搭配方得建構完整之老年經濟安全保障體系。 我國勞動基準法中規範之退休金給付辦法，賦予企業給付退休金之義務，而此義務係屬之企業經營成本，在尚未制訂一套公認準則時，企業實務上多按所得稅法第33條為相關之退休金會計處理，係以當期提撥之退休金準備或提撥之退休基金作為當期退休金費用，導致財務報表無法公正允當的表達。證管會有鑑於此，乃委託中華民國會計研究發展基金會制訂第十八號公報「退休金會計處理準則」，明訂企業應於財務報表中充分揭露退休金之提撥狀況，避免企業藉由退休金提撥的手段而操縱損益。第十八號公報雖未規範企業應如何提撥退休基金，但已明訂相關退休金費用、退休金負債等項目應於財務報表上列示、揭露，故公報之實施勢必會影響企業之提撥策略，因此，本研究試圖瞭解公報實施前、後與勞基法賦予企業退休金給付義務間之關聯性，是否會因公報之實施而改變企業之退休金提撥策略。除此，對於不同性質之企業於決定退休金提撥水準是否有所差異？一般企業提撥退休金考慮之因素為何？及勞委會擬定之「勞工退休金條例草案」與現況制度比較等問題作一探討，相信本研究將有助於進一步架構我國完整之老年退休保障制度。

本研究基於退休基金經理人之觀點探討確定提撥退休基金計畫之跨期最適投資策略，分析退休計畫中成員薪資所得不確定以及跨國投資風險對於基金投資決策的影響。首先，由於匯率之波動將顯著增加跨國投資收益之風險，本研究引用Xia (2001)考量學習效果預測跨國匯率過程，修正匯率之動態隨機過程；搭配跨國費雪關係式進一步假設國內為名目利率差與匯率的關係式，使得投資策略得以納入匯率的學習效果。其次，薪資所得波動對於提撥有所影響，因此本研究推廣Boulier et al. (2001)對於成員勞動薪資之假設，假設通貨膨脹率及實質利率將影響成員服職期間之薪資所得，基金經理人將策略地調整基金投資標的物之部位以規避成員薪資風險。最後，本研究呈現完整之跨期投資策略及詳細之數值計算結果，清楚說明退休基金經理人於追求最適投資組合及避險考量之關係。研究結果顯示，基金經理人可以透過資本市場消弭薪資所得的不確定性，而匯率的學習效果將影響在國外現金部位的變化。

本文利用隨機控制理論，延續Chang et al. ( 2002 )，採用總和精算成本法，考慮提撥率風險( Haberman and Sung ( 1994 ) )極小的情況下，推導確定給付退休基金之最適提撥與資產配置策略封閉解，資產配置部分考慮股票市場投資組合、永續債券、現金三種部位。 套用公務人員退撫基金第四次精算報告之數據，透過Matlab重覆模擬1,000次，數值結果如下： 1.正常成本與提撥金額呈遞增趨勢，且兩數據差距甚小，符合風險評估函數所設定之提撥率風險極小化的要求。十年控制期間中，正常成本成長5.32倍，從1.03億增加至5.49億；提撥金額成長16.65倍，從0.33億增加至5.56億。275期以前正常成本大於提撥；275之後提撥大於正常成本。 2.初期提撥金額小於給付金額，且投資報酬不足以彌補其差額，因此造成基金規模縮小，但由於提撥金額成長速率大於給付支出，使得基金規模下降程度趨緩，隨後開始穩定成長。十年控制期間中，基金規模從起始的1,000億下降至840億，再上升至約1,314億。 3.股票與債券之持有或放空的部位越多，基金報酬率波動越大，基金規模越大時，可承擔風險的容量增加，因此傾向高風險投資；基金規模越小時，風險承受度變小，所以投資策略反而趨向保守。股票最多持有99.18%、放空90%；債券最多持有293.5%、放空140.14%。 / In this study, we continue using the model of Chang et al. ( 2002 ), which is based on stochastic control theory to study the dynamic funding policy and investment strategy for defined benefit pension plans. The model includes three investable assets: stock market portfolio, consol bond, and cash. We apply “Aggregate Actuarial Cost Method,” so only the contribution rate risk proposed in Haberman and Sung ( 1994 ) is considered when measuring the performance. In addition, we analyzed the data from Taiwan Public Employees Retirement System (Tai-PERS) investigate the optimal contribution and asset allocation through the proposed model and arrived at the following conclusion: 1.The trend of increasing normal cost and contribution as well as the small disparity tally with the requirement of minimum contribution risk as defined in the loss function. 2.In the beginning, the return of investment and contribution are insufficient to cover the benefit payment, causing the fund level to shrink; but as the rate of contribution increases over time and surpasses the benefit payments, the fund level will cease to shrink, and start to grow gradually. 3.There is a positive correlation between the fund level and the risk of investment. In other words, the larger the size of the fund level, the higher the possibility of holding or short selling risky assets.

論文摘要: 本研究以現金餘額計劃（Cash Balance Plan）及確定提撥退休金計劃（Defined Contribution Pension Plan）建構出公務人員退撫基金之建議機制，建構之主要目的在於透過第一層現金餘額計劃之利息給付機制降低退休基金利率風險，同時由第二層確定提撥計劃獲取額外退休所得，使雇主與員工在双層式退休金計劃下，同時承擔投資風險，以降低基金利率風險並同時滿足適當退休所得保障。本文在現金餘額計劃不同控管年限及利息給付假設下，模擬超額積蓄（Overfunded）基金與不足額積蓄（Underfunded）基金執行資產負債管理（Asset Liability Management）所需存續期間，同時模擬双層式退休金計劃提供員工之退休所得替代率，研究結果發現： 1、超額積蓄基金及不足額積蓄基金均可以在目前資本市場中找到符合所需存續期間之資產投資。在控管20年限內，超額積蓄基金所需存續期間在-1.71年到0.39年之間；不足額積蓄基金所需存續期間在4.68年到8.31年之間。 2、退休基金越接近超額狀態越有利於資產負債管理。當基金積蓄狀態越接近超額積蓄時，基金負債與資產的比例較不足額積蓄基金低，故資產負債管理所需存續期間較短，對於基金能夠控管的年限也越長。 3、雇主可透過現金餘額計劃利息給付機制執行百分之百免疫策略。雇主可利用現金餘額計劃利息給付依據外部債券利率為參考依據的特性，鎖定債券利率，達到資產負債管理百分之百免疫效果。 4、現金餘額計劃執行百分之百免疫策略情況下，45歲以下公務人員採行自動選擇投資基金（Default Fund）為高風險投資基金，自動選擇提撥率（Default Rate）為每月薪資5.08﹪，可使員工達到適當所得替代率保障水準。 / Abstract This thesis proposes an new alternative two-tier pension composed of Cash Balance Plan (CBP ) and defined contribution pension plan to the traditional defined benefit pension plan of Taiwan Public Employee Retirement System(TPERS). In order to decrease the interest-rate risk of the pension fund and to provide additional retirement income protection, we utilize the credit rate mechanism of CBP and supplement CBP with additional defined contribution plan. We investigate the Asset-Liability Management (ALM) for TPERS and calculate the liability duration under different time horizons, interest credits of CBP. We also simulate the replacement rate of the two-tier pension plan under different contribution rates, and investment returns. The results are as follows: 1、Given the twenty-year time horizons, the asset duration of overfunded plan ranges between –1.71 years and 0.39 years, whereas that of underfunded plan varies from 4.68 years to 8.31 years. In this case, the requirements of asset duration can be satisfied in the Taiwan Capital Market. 2、The overfunded pension plan has higher probabilities to meet the requirements of asset duration. Therefore, we suggest that the fund manager can increase the asset allocation percentage of external fund management in order to improve the long-term returns. 3、Perfect matching of pension fund can be achieved by matching the yield of securities to interest credit under CBP . In addition, we suggest that the interest credit of the new labor contracts should take the trend of the current interest rate into consideration. 4、Replacement rates provided by CBP for woman range from 19.05﹪ to 45.70﹪and from 20.86﹪to 50.05﹪for man assuming the interest credit rate is 5.2%. To increase the retirement income, the defined contribution plan provide additional replacement rate between 13.56﹪and 162.96﹪for woman and between 14.85﹪and 178.42﹪for man assuming the employee can contribute 3.08 percent to 13.37 percent of regular salaries and investment returns are from 4 percent to 8 percent .

我國65歲以上的老年人口，於民國82年底達總人口比率7.1％，正式邁入聯合國世界衛生組織所稱之高齡化社會（7％以上）。根據行政院經濟建設委員會之推估，65歲以上的老年人口比例於97年將達總人口數之10.15％，而於116年達總人口數之20.04％，人口老化速度明顯高於歐美國家，未來人口年齡結構將更趨於高齡化。隨著我國老年人口成長，社會安全制度日益受到重視，提供老人經濟安全之適度保障將成為我國未來福利發展之新方向。 本研究根據世界銀行提出的「三層保障」之老年經濟安全保障制度架構為基礎，說明我國公務人員退休制度在老年經濟安全保障方案之定位，闡述有關第二層保障之職業退休金制度理論演變，以釐清公務人員退休金之屬性及正當性，以助於退休制度及其財務規劃的擬定，期使整套制度循著適當的理論脈絡而發展。基於對退休金重要性的認知，先進國家早已發展成熟的職業退休金制度，而我國公務人員退休制度係建制於民國32年，實施50餘年，雖歷經4次修正，由於退休金給付方式仍屬於恩給制，除造成財政上重大負擔外，也產生退休給與偏低等嚴重問題，相關機關自62年開始研究改革，經過22年研議規劃完成，自84年7月1日實施退休新制，其與舊制最大的差異，是將退休經費籌措方式，由政府編列預算支付之恩給制，改由政府與公務人員共同撥繳費用成立退撫基金之共同提撥制，其餘退休對象、退休年資、退休條件、核給退休金原則大致維持不變，而退休金給付方式，也維持著確定給付制。經分析新退休制度之主要內容，實施迄今8年餘，有關改進退撫經費籌措方式，減輕政府財政負擔；及提高退撫所得，加強安老卹孤之改革目標，均已獲致初步成效。然而現階段面臨之問題，是退休經費導致各級政府財政負擔增加，且依公務人員退休撫卹基金管理委員會委託基金精算結果也顯示基金將面臨財務危機。 本研究係分析新制退休金給付方式，全面採行確定提撥制，對解決基金現存財務危機之可行性，為便於瞭解，爰敘明確定提撥制與確定給付制之意涵與優、缺點，及我國採用此兩種制度之適例。茲因退休金給付方式之政策變革方案，影響層面甚廣，方案之可行性如何，必須審慎探討與分析，爰就制度變革方案可行性列舉幾項評估面向進行分析。 例如為解決基金財務問題，除必須從經濟上分析外，茲因制度變革方案，必須符合現時的政治生態，始能確保政策推行之成果，方案的周詳與否，關係到該方案能否被接受及未來能否順利執行。由於退休舊制恩給制時期，因退休經費籌措方式不當，同樣存在著財政負擔之問題及缺失，其能於84年7月改革成功推動新退休制度，在政治方面包括政黨、民意機關、相關主管機關、公務人員，甚至學者等等支持的因素，在現今新制推行後，為解決財政問題，而將退休金給付方式，全面改採確定提撥制，是否同樣具有政治上支持的可能性，自須審慎分析；此外，退休金政策之改變，直接受影響的便是公務人員之退休所得，在退休金採行確定提撥制後，是否仍能達成新制推行時所設定之提高退撫所得、加強安老卹孤改革目標，應為關鍵之所在，由於職業退休金理論中之維持適當生活，係本研究在規劃退休金制度時所考量的重點，因退休後的生活水準應能與退休前相當，乃是探討退休金制度的核心，爰列為評估面向。又世界各國實施公務員退休金制度之經驗，包括採行確定給付制與確定提撥制例證，及面臨困境或改革之趨勢，均能在我國制訂退休金政策時有所啟示，故亦列為評估面向。本研究依據上述重要項目進行整體性評估，針對現存政經環境及職業特性，歸納我國新制退休金採行確定給付制或確定提撥制之個別效益，深入檢討何種給付方式較能維持公務人員權益？及退休前之生活水準？藉以說明並支持可行方案，以作為方案選擇之參據。最後提出本研究之結論與研究發現，進而本於基金能否永續經營，將是制度得否存續的關鍵，減少財務潛在危機，應具有合理的制度設計與有效的經營管理之基本條件，爰研擬若干建議措施，以降低財政問題的嚴重性，俾確保基金日後退休給付之能力，保障參加基金人員之權益。 / Taiwan has officially joined the “aging society” as defined by the WHO (up to 7% of the senior citizen ratio) because senior citizens aged over 65 accounted for 7.1% as of December 31, 1993. The official forecast by the Council of Economic Planning & Development of the Executive Yuan (the Cabinet) indicates that the senior population age over 65 will hit 10.15% of the total population by 2008 and even up to 20.04％ by the year 2027. Taiwan significantly outpaces their European and American counterparts in terms of the ratio of aging citizens. The aging society problems will likely turn from bad to worse in the future. In turn, the social security system is receiving mounting awareness and attention. The efforts to provide sound financial standing, secured social systems and protection to senior citizens will represent the new orientation of future welfare development in Taiwan. The present study takes the “Three-Level Assurance” oriented senior citizen financial security system proposed by the World Bank as the very grounds to elucidate the positioning of the Public Servant System in the senior citizen financial security system, annotate the evolution pension system of the Second-level Assurance to clarify the attribute and justification of the pension granted to civil servants. The present study is intended to help draw up a retirement system and financial planning so that the entire system will develop toward appropriate and justified orientation. With awareness of the importance of pension, those advanced countries have developed sound and mature professional pension systems for quite some time already. In the Republic of China, the retirement system for civil servants was initiated in 1943 and has been updated four times during the subsequent half century. The pension has been granted as a sort of benefit, or a government favor. As a result, pension to civil servants has become a heavy financial burden to the government and has been illogically insufficient. In response, the competent authorities concerned began initiating research for a reform of the pension system in 1973 and completed the research program 22 years later. The new retirement system was officially put into place on July 1, 1995. Between the old and new retirement system, the greatest difference is that the pension fund is jointly contributed by both the government and civil servants themselves in the new system instead of being solely budgeted by the government as a sort of government favor in the old system. Except for this, the aspects of the target retirees, seniority requirements, prerequisites for retirement and the principles to grant pension largely remain unchanged. Pension is paid in an unchanged “Defined Benefit Plan”. Now, with the new system in enforcement for over eight years, the new system proves to have primarily attained the goals in improving the method of pension fund raising, easing up the government’s financial burden, providing added pension to retirees and better safeguarding the senior civil servants. The problems currently confronting the pension practice are largely the mounting financial burden to the government as incurred by the retirement expenses. Meanwhile, the actual calculation outcome consigned by the Pension Management Committee indicates that the Pension Fund is on the verge of financial difficulties. The present study is to analyze the terms of pension payment to determine the feasibility there-of and to solve the present financial problem by means of the “Defined Contribution Plan”. For better a understanding into the issues, the present study elucidates the connotation, strengths and weaknesses of the “Defined Contribution Plan” and “Defined Benefit Plan”, as well as the precedents in Taiwan in adopting such two systems. Where a reform in the policy of pension payments will create quite an extensive impact, the feasibility of the policies calls for prudent analysis to enumerate a few feasible alternatives before further analyses into a few aspects of the assessment. To solve the financial difficulties in the Pension Fund, for instance, other than the economic analyses, the reform of the system must live up to the current political ecology before it can ensure the effects expected through the enforcement. Whether or not the policies are detailed and comprehensive enough will determine whether or not the policies are acceptable and whether or not they can be put into successful enforcement without a ensuing problems. During the extended practice under the old system while pension was budgeted as a sort of government favor, the pension system led to a heavy financial burden and shortcomings on the government. The new pension system was successfully put into enforcement in July 1995, thanks to the unanimous support from the political parties, congress, competent authorities concerned, civil servants as well as scholars. Now, in an effort to solve the current financial problems under the new system, the pension will be paid under the “Defined Contribution Plan”. Will the present reform receive equal political support? It calls for well-advised analyses. Besides, in a change in the pension system, the top impact will be upon the pension income to civil servants. After the pension is under the “Defined Contribution Plan”, will civil servants receive added pension income and receive better security in their retired life? These will be the key issues under the present study. The core consideration should aim at the retired lifestyle, which should be equivalent to the pre-retirement one. The hands-on experiences in enforcing civil servant pension systems accumulated in other countries the world over, including precedents of their practices in adopting the “Defined Benefit Plan” and “Defined Contribution Plan” will function as the constructive examples in Taiwan’s policymaking process regarding pension systems, and will be, therefore, be covered in the assessment in the present study as well. The present study will launch an overall assessment on the aforementioned key issues. Aiming at the existent political and economic climate as well as the professional characteristics, the present study will generalize the individual effects and benefits under “Defined Benefit Plan” or “Defined Contribution Plan” under the new retirement system to find out the optimal terms of payment to assure maximum possible benefits to civil servants, safeguard the quality of their retired lifestyle to be equivalent to the pre-retirement lifestyle. The findings and conclusions yielded through the present study will function as handy reference materials for policymaking. By submitting the findings and conclusions so yielded, the study will help the policymakers draw up sound enforcement rules to ensure the sustained existence of the Pension Fund, alleviate the potential financial crises through reasonable design of systems and effective management as the very fundamentals. Further by offering constructive proposals, the study will help the competent authorities of the government solve the financial difficulties to ensure sustained sound competence of pension payments and to, in turn, safeguard the Pension Fund and the Fund’s beneficiaries.

為使台灣公部門能利用確定提撥的概念及妥善運用投資資源，以期在減少政府負擔的情況下獲得足夠的退休所得，故本研究以所得替代率、金錢價值比及平均數-變異數比等指標來針對公務人員退撫基金附加節約儲蓄制度採行之可能與投資策略彼此運用之模擬結果加以分析，結果如下： 1. 各情境下以BH策略所得出之期末個人帳戶平均累積值表現最佳，然其具相當大的波動變異程度，投資人需承受相當大的風險。而TIPP策略之表現則與前述完全相反。 2. 若投資者採用BH策略或是採用CPPI與TIPP策略(CM策略)且欲追求較高的所得替代率，則建議採用Lifecycle(平衡型)的投資比例配置方式，加計DB制下之給付則平均可提供男(女)性約70.204%-75.204% (65.49%-70.49%)的所得替代率，而金錢價值比則為2.399(2.95)。 3. 無論投資者採用何種策略進行投資，若欲追求最小的可能變異風險，則建議採取平衡型的投資比例配置方式，加計確定給付制下之給付則平均可提供男(女)性約67.924%-72.924%(65.318%-70.318%)的所得替代率，金錢價值比則為2.6835。 本文模擬結果所得出之所得替代率平均維持於70%上下，代表若政府將可藉此制度減輕政府負擔外亦可使員工擁有一定水平的退休生活，故可採用。至於投資策略與配置方式如何取捨須依不同的投資者而定。 　 關鍵詞：公務人員退撫基金、確定提撥制、所得替代率、金錢價值比、Lifecycle / Abstract Because the improvement of medical technology and the structure of population is aging. It makes human worry about the living in the future. In order to enable the public servants of Taiwan to utilize the system of the Defined Contribution and to relief the pressure of fiscal, so we simulate in this article and analysis the results of simulation by using replacement rate, money’s worth ratio, and mean-variance ratio. The result is as follows: 1.When investor adopt the BH strategy in the process of investment, it will create the best replacement rate and money’s worth ratio under every situation, but it can be anticipated more uncertainty. Investors need to think thrice before they act. The TIPP strategy is opposite. 2.If investors adopt BH strategy or CPPI and TIPP strategy (CM strategy) and wanting to pursue the substituting rate of the higher income , the best selection is proposed adopting the Lifecycle (balanced) scenario, and it can offer replacement ratio about 70.204% - 75.204% (65.49% - 70.49% ) for the man (the woman ) under adding the DB system. Besides, the money’s worth rate is 2.399 (2.95). 3. If the investors want to pursue the least influence in the process of investment whatever investors adopt which strategies, the best scenario is the balanced type, and it can offer replacement ratio about 67.924%-72.924%(65.318%-70.318%) for the man (the woman) under adding the DB system. Besides, the money’s worth rate is 2.6835. The outcome of the simulation in this article is keep the replacement rate maintain about 70% equally, What is the best selection for investor that must be contingent upon different characteristics of investors. Keywords: public servants, Defined Contribution, Replacement rate, The money’s worth ratio, Lifecycle hypothesis.

本研究主要分為三個部分：第一個部分探討壽險公司保單組合之最適資產配置；第二個部分探討確定提撥退休金制度下，員工所面臨的資產配置問題；第三個部分則為方法論的比較研究。此外，本文也探討長命風險(longevity risk)等相關議題。本文在Huang與Cairns (2006) 所提出的資產報酬模型下，推導出累積資產價值的期望值以及變異數，並利用套裝軟體的最佳化程式(optimization programming)獲得給定目標函數下的最適投資策略。 在保單組合資產配置之研究方面，我們分別針對保險公司繼續經營的商品以及即將停賣的商品提出合適的資產配置方式。常數資產配置方式(Constant rebalance rule)適合持續經營的商品，變動資產配置方式(Variable rebalance rule)則適合即將停賣的商品。在常數資產配置方式下，我們能夠得到投資組合的效率前緣線。此外，不管是何種資產配置方式，當保單組合的保單到期日較近時，保險公司必須增加其所持有的現金比例。 在確定提撥制下最適資產配置問題的研究方面，本文的結果符合一般退休基金經理人所採取的生命週期型態投資方式。本研究發現在Lee-Carter模型之下，考慮時間加權可以增加模型的預測能力。而在考慮長命風險下，員工必須採取更積極的投資策略。 本文決定資產配置之方法為預期模型(Anticipative model)，其在評價日時即決定未來的決策，不考慮新訊息對決策的影響。考慮新訊息會對決策產生影響的決定資產配置方法為適應模型(Adaptive model)。在第五章的研究裡，我們比較上述兩種決定資產配置方法之差異。研究結果發現，若以期望值與標準差為判斷標準，兩種決定資產配置方法並沒有絕對的優劣關係。而若在每個決策執行的時間點重新使用預期模型來決定新的資產配置策略，則其所對應的投資策略以及投資績效會與適應模型下的策略與投資績效接近。因此，在無法獲得適應模型投資策略封閉解的情況下，預期模型投資策略可以有效的近似適應模型投資策略。 / The purpose of this thesis is to investigate the asset allocation issue of the long-term investors. Our approach is to calculate theoretical formulae of the first two moments of the accumulated fund; we then adopt optimization programming to find a asset allocation strategy that fits the fund management target. Two kinds of investors are explored. The first one is an investment manager who manages a general portfolio of life insurance policies, and the second one is an employee who starts his career life in a DC pension plan. We also survey the longevity risk issue in this thesis. In the study of “optimal asset allocation for a general portfolio of life insurance policies”, two kinds of rebalancing methodologies are examined. For constant rebalance rule, which is applicable to a continuing business line, we find an efficient frontier in the mean-standard deviation plot that occurs with arbitrary policy portfolios. Also, the insurance company should hold more cash to reduce its illiquidity risk for portfolios in which policies will mature at earlier dates. In the study of “optimal asset allocation incorporating longevity risk in defined contribution pension plans”, we confirm the suitability of the lifestyle investment strategy. Investors in a DC pension plan should be more aggressive when he considers the longevity risk. Furthermore, we proposed a time adjustment technique to capture mortality predictions more precisely in this study. The approach of decision making of this thesis is referred to anticipative model, which does not consider the possible feedback from the future information. On the other hand, the approach of decision making that consider the possible feedback from the future information is referred to adaptive model. We further compare the two approached in the study “Comparative efficiency- anticipative model versus adaptive model”. The numerical results show that investors would not prefer the adaptive approach to the anticipative approach in the mean-variance criterion. Moreover, the downside risk is larger when the strategy is decided by adaptive approach. We also find that the strategy and its numerical distribution of anticipative approach can approximate to that of adapted approach if one re-assesses it at every decision date. Thus, the anticipative approach provides a first approximation on looking for the optimal investment strategy of adaptive model.

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.