聯合國以老年人口佔總人口數百分之七作為老人國分類標準的比率,依據我國六十五歲老年人口截至民國八十二年九月底已佔總人口7,02%,顯示我國已正式邁入高齡化國家。政府為了解決高齡化社會所將帶來的老人生理方面和經濟方面的問題,已於民國八十四年三月一日起,實施全民健康,保險制度,以提供老年人部份的醫療需求;並擬規劃開辦國民年金保險,以提供老年人基本經濟生活之保障。國民年金保險為一種長期性的社會保險,故制度是否能健全,就緊檕於整體性的長期財務規劃是否完備。綜觀目前已實施國民年金保險制度的先進國家,大多因先其前財務規劃未盡健全,以致年金財務會發生危機,也造成了政府財政上的負擔。因此在國民年金險制度研擬規劃之初,本文欲藉著模擬分析方法加以研究,以提供可行之財務制度及制度財務狀況。

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.

確定給付制的退休金計畫，退休金成本提存的適當與否，關係到基金長期的財務健全及未來員工權益的保障，而我國公務人員退撫基金關係到廣大公務人員的權益，也影響到政府的財政支出，所以對公務人員退撫基金更有精算的必要，以確保提撥率之適當而不至於對政府財政增加額外負擔。 本論文從人口面的角度出發，以我國公務人員退休撫卹基金為實證分析之研究對象，探討人口面的假設對於公務人員退撫基金提撥率，未來各項給付支出的影響，包括從經驗資料中取樣，探討大小不同的樣本建立之服職表，於計算提撥率的差異，並利用混成模型建立新進成員假設，以開放團體模擬基金成員結構，在某些固定假設之下，模擬未來五十年的基金資產與現金流量情況。 根據本研究結果指出，利用不同取樣所建構的服職表，計算出之提撥率差異甚大，顯示小型的退休金計畫並不適宜以自身的經驗資料作為精算評價的基礎。另外，以常態分佈的混成模型建立公務人員新進假設，在人數設限成員群體的假設下作開放團體模擬的結果，顯示公務人員年齡結構在未來有逐漸老化的趨勢，在本文所採的假設下，基金資產將先增後減而於民國121年破產。在現行的公務人員退休撫卹制度下，要避免基金破產之情況發生，唯有提高提撥率、提高基金資產報酬率、或壓低薪資成長率。 第一章 緒論 第一節 研究動機與目的 第二節 研究範圍與限制 第三節 研究架構與內容 第二章 退休金精算考慮之因素 第一節 退休基金精算系統的概念及文獻回顧 第二節 精算假設 第三節 精算成本法 第三章 基金成員結構分析的理論基礎 第一節 服職表的編製 壹、 模型建立 貳、 修勻方法 參、 程式演算過程 第二節 混成參數模型的建構 第三節 基金成員新進參數模型的建立 第四節 基金成員新進、脫退隨機過程 第四章 公務人員退撫基金精算模擬 第一節 公務人員退撫基金給付規定 第二節 公務人員退撫基金精算評價系統簡介 第三節 公務人員退撫基金精算評價之實證 壹、 取樣差異對於提撥率的影響 貳、 開放團體模擬基金成員結構和財務預估 第五章 結論與建議 第一節 結論 第二節 對後續研究的建議 附錄A：估計粗脫率之程式 附錄B：修勻程式(Whittaker法) 附錄C：估計常態混成模型參數之程式 附錄D：公務人員新進成員年齡、職等分佈模擬之程式 附錄E-1：服職表1 附錄E-2：服職表2 附錄E-3：服職表3 附錄E-4：服職表4 附錄E-5：服職表5 附錄E-6：服職表6 附錄E-7：服職表7 / The adequacy of the plan contribution for a defined benefit pension scheme is directly related to its financial soundness and the plan member’s benefits. Due to uncertainty of the plan’s turnover, the service table plays an important role in actuarial valuation and cash flow projection. In this study, Taiwan public employees retirement system is studied to monitor the solvency issue due to bias in selecting the service tables. Tai-PERS is designed to provide retirement and ancillary benefits to 271,215 government employees. Its financial soundness is especially vital to the government annual balance. The plan contribution and projected cash flows of Tai-PERS are investigated using various sampling results. The distribution of the new entrants is assumed to follow the mixture model to describe the recruiting results. Then dynamic simulations under the open group assumption are performed to predict the future fund assets and cash flows. The results show significant differences in employing various service tables. Hence selecting proper demographic assumptions is particular important in pension valuation. Under our approach, the workforce of Tai-PERS is aging given the current plan population. Based on the given scenario, the projected plan assets increase and then decrease to be insolvent in 2032. Some interesting results are also discussed.

退休金計畫依給付方式的設計，可以分為兩大體系：確定給付退休金計畫與確定提撥退休金計畫。無論是公共退休金計畫或是企業退休金計畫，最初實行時多採用確定給付的方式來實施。但隨著經濟環境的變遷，部份的國家與企業雇主，已開始傾向確定提撥方式的採用。本論文有鑑於退休金的改革潮流，欲探討確定提撥退休金計畫的實施回顧與給付的精算分析。 本論文分為四個主要部分，分別為：(1)確定提撥計畫的理論架構回顧；(2)主要國家制度的分析；(3)精算模型的建立與精算假設的分析；與(4)精算假設的給定與給付水準的模擬分析。在主要國家制度的回顧上，公共退休金計畫方面以新加坡「中央公積金制」與智利「公共退休金私有化」為探討的對象；在企業退休金計畫方面則以美國為討論對象。實證分析部分，則是先建立確定提撥退休金精算模型，再撰寫模擬程式介面，並以我國1998年「勞工退休金條例」草案為模擬對象，給定精算假設進行模擬，最後分析精算假設與模擬給付間的關係。 以台灣「勞工退休金條例」草案為例進行分析，其實證部分分為兩部分，先前給定平準的預定利率假設，而其他薪資成長率、通貨膨脹率、提撥率、開始工作提撥年齡、退休年齡、退休後各年存活率則根據台灣目前的經濟、就業環境給定；模擬結果發現， 6％合併提撥率無法達到模擬所給定50％-60％的退休後給付所得替代率；若將合併提撥率提高至12％以上，25歲開始工作65歲退休者才能累積足以支應適足所得替代率50％-60％的給付。 第二個模擬部份為給定利率時間序列的情境假設，在此給定簡單的七種利率情境假設，其他精算假設則同樣根據台灣的經濟環境給定之。模擬結果發現，若合併提撥率為9％，基金提撥累積期間40年，給付所得替代率對利率的變動敏感性高，只有在累積期間利率穩定成長的情形下，才能累積足夠的退休金，因此，可以表示9％的合併提撥率在其他非樂觀的利率情境假設下，無法達到50％-60的給付所得替代率。 略 / Due to population aging, the countries that operated their Social Security System on pay-as-you-go financial method have begun to encounter the solvency risk due to the growing financial burden. Since the defined contribution (DC) scheme is considered as a fully funded financial system, it could be one of the solutions to avert the upcoming financial crisis. Hence our study is motivated to investigate the current development of the DC scheme and scrutinize its financial adequacy on providing the retirement benefits to its plan participants. First, the features of current public pension programs in the form of the DC plan are surveyed and their progress is reviewed in Chapter 2. Practical applications applying the DC scheme in private sector are also compared and studied in Chapter 3. Secondly, the actuarial models of the proposed DC scheme are built to investigate the adequacy of the retirement benefits in Chapter 4. Computer codes that can be used to simulate the income-replacement ratios by giving the actuarial assumptions are programmed. Based on this approach, the relationship between income-replacement ratios and the actuarial assumptions (i.e., the interest rate, the salary increase and the inflation rate) can be obtained. In Chapter 5, sensitivity analyses of the benefit adequacy through computer simulations incorporating possible scenarios are performed. The recent proposal of reforming Taiwan Employee Retirement Income Security Act (TERISA) is investigated. An explicit actuarial model closely following this proposal is built to study its impact on the retirement benefits. Finally the empirical results based on this study are summarized. Based on the scenarios under the current economic perspectives, we found the contribution rate at 6% can not attain the income-replacement ratio at 50%. Only over certain optimal interest rates, the retiree can receive the projected income-replacement ratio given the contribution rate at 9%. Based on the proposed draft in reforming the benefit scheme, the retirement benefits are not sufficient to achieve the income-replacement ratio at 50% unless the contribution rates increase to 12%.

退休金的會計處理原本即具複雜性，加上最近退休金制度的變革，形成退休金會計獨特且豐富的情境背景，提供了許多的研究機會。本論文包含三個與退休金會計相關之議題；其中第一個議題是「勞工退休金新制之股價效應」；第二個議題是「退休金精算假設選用之誘因」；第三個議題是「退休金精算假設選用之價值攸關性」。三個議題均以效率市場假說為基礎，針對勞工退休金新制之實施與退休金精算假設之選用，分別深入探討其與股價之關聯性。 首先，本論文第一個議題探討勞退新制之股價效應。事件日股票報酬與公司特質的關聯分析，雖然部分的實證結果不顯著，然而部分的證據顯示，勞退新制公布實施時，公司股票報酬與退休金提撥不足程度、員工平均服務年資、退休金提撥率、退休金成率等公司特質具有關聯性，隱含資本市場在某種程度上，似乎可以依據勞退新制對公司不同之衝擊程度，反映於公司股票報酬。 其次，本論文第二個議題探討退休金精算假設選用之誘因。實證的結果顯示，我國上市上櫃公司精算假設選用的橫斷面差異，可能源於債務契約、提撥不足之成本以及損益平穩化等誘因。最後，本論文第三個議題探討退休金精算假設選用之價值攸關性。實證結果顯示，退休金精算假設選用具價值攸關性，投資人對公司選用精算假設保守程度有所評價，對於裁量性 (隱藏的) 預計給付義務亦有所反映，似乎適當地根據精算假設選用對於預計給付義務之影響幅度來調整對公司之評價，隱含資本市場並未功能性固著於報導的退休金義務。 / There are three essays in this dissertation. The first essay examines the impact on equity prices of the Promulgation of Labor Pension Act. Evidence reported in the paper shows that negative abnormal returns are most pronounced for firms with large underfunded level of pension plan, firms with little average years of employment, firms with low contribution ratio, and firms with low pension cost ratio. The second essay explains the cross-sectional variation in firms’ selected actuarial assumptions (rate of increase in compensation and discount rate) used to measure the projected benefit obligation (PBO). Evidence shows that firms with relatively larger debt ratio, larger underfunded level of pension plan, and larger decline in earnings tend to select more aggressive (obligation-reducing) estimation parameters. The last essay studies the association between actuarial assumptions and firm value. The results indicate that firm value is lower, conditional on the reported PBO, for firms that use higher discount rates and lower rate of increase in compensation. This is consistent with investors seeing through managers’ opportunistic choices of obligation reducing assumptions. The evidence suggests that the stock market does not fixate on reported PBO numbers, but properly appreciates the value relevance of the discretionary component of the PBO.

本研究以確定給付型退休基金為對象，建構廣義隨機評價模型，以衡量不確定情況下退休基金之財務風險。希望藉著模型建構的過程，適切地描述基金評價過程中所應考量的各項要素。 為了強調基金評價時同時考量內外部精算假設的重要性，本研究將模型分為存活函數、經濟函數和給付函數三部份討論；存活函數利用離散時間非同質性半馬可夫過程（Discrete Time Non-Homogeneous semi-Markov Process）描述成員狀態轉移的機率，把成員工作年資、年齡和及狀態納入評價過程，有別於傳統僅以年齡為假設基礎之精算方法；經濟函數則以隨機過程表達外部環境的不確定性，結合上述假設資訊預估未來給付後，成為半馬可夫隨機精算評價模型，此一般性的模型能推展至基金評價時所需的各項流程。因此，本研究將模型應用於我國公務人員退撫基金，針對公務人員退撫基金的給付特性發展財務評價公式，完整地描述基金精算成本計算、未來人力與現金流量結構模擬以及敏感度分析等過程。 最後，本研究撰寫公務人員精算評價資訊系統，具體化半馬可夫隨機精算評價模型，實證公務人員退撫基金財務評價公式。實證結果也顯示，不論基金的性質或外部經濟環境，都將影響退休基金財務評價結果，為基金評價時不可忽略的精算假設。 / This study focuses on constructing a generalized valuation model for the defined benefit pension schemes. Financial soundness and funding stability are critical issues in pension fund management. In this study, a realistic stochastic model is built to monitor the uncertainty factors in affecting the financial risk and cash flow dynamics along the decision process. In order to evaluate the importance of the interior and exterior actuarial assumptions in pension valuation. Detailed models in describing the turnover patterns, economic uncertainties and benefit structures are explored. Semi-Markov process proposed by Dominicis, Manca and Granata (1991) and Janssen and Manca (1997) is extended in structuring the transition pattern of the plan’s population and the economic based factors are generated through stochastic processes. Modifications according to classification and movements of the plan member and the plan’s turnover pattern are employed to improve its practical usefulness. Then the actuarial valuations, cash flow analyses and workforce projection are performed and investigated. We has explicitly formulated the plan’s realistic phenomenon and implemented the proposed mechanism into a risk management framework for pension finance. By using this realistic approach, the cost factors could be monitored throughout the valuation. Typically these analyses involve substantial assumptions. This article has outlined the procedure of building the proposed model. Finally, Taiwan Public Employees Retirement System is simplified to illustrate the proposed methodology in pension valuation. The results from this study show that the structure of the pension schemes and the assumed economic factors are the significant factors in pension valuation. It also indicated that the fund manager can evaluate these impacts through the proposed model.