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研究生:葉倩妏
研究生(外文):Yeh,chien wen
論文名稱:確定給付退休金計畫於總和精算成本法之最適控制
論文名稱(外文):Optimal Control of the Defined Benefit Pension Schemes under Aggregate Actuarial Cost Method
指導教授:張士傑張士傑引用關係
學位類別:碩士
校院名稱:國立政治大學
系所名稱:風險管理與保險研究所
學門:商業及管理學門
學類:風險管理學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:中文
論文頁數:50
中文關鍵詞:最適提撥資產配置總和精算成本法
外文關鍵詞:optimal contributionasset allocationaggregate actuarial cost method
相關次數:
  • 被引用被引用:1
  • 點閱點閱:279
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
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.

摘 要 2
英文摘要 3
目 錄 4
圖表目錄 5
第一章 緒 論 6
第一節 研究動機與目的 6
第二節 研究方法 7
第三節 台灣退休基金 9
第二章 文獻回顧 13
第三章 財務模型 16
第一節 符號說明 16
第二節 模型推導 18
第四章 數值結果 29
第一節 模擬步驟說明 29
第二節 模擬結果 35
第三節 小結 39
第五章 結論 41
參考文獻 43
附 錄 48

英文部分:
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Campbell, J.Y. and Viceira, L.M. Strategic Asset Allocation, 2nd ed. Oxford University Press, 2003.
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Boulier, J.F., Trussant, E., and Florens, D. “A dynamic model for pension funds management.” Proceedings of the 5th AFIR International Colloquium 1 ( 1995 ): 361–384.
Boulier, J.F., Michel, S., and Wisnia, V. “Optimizing investment and contribution policies of a defined benefits pension fund.” Proceedings of the 6th AFIR International Colloquium 1 ( 1996 ): 593–607.
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Brennan, M.J., Schwartz, E.S. “The Use of Treasury Bill Futures in Strategic Asset Allocation Programs,” In Worldwide Asset and Liability Modeling. (J.M. Mulvey and W.T. Ziemba, Eds.) Cambridge England: Cambridge University Press, ( 1998 ): 205-230.
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Cairns, A.J.G. “Pension Funding in a Stochastic Environment: The Role of Objectives in Selecting an Asset-Allocation Strategy,” Proceedings of the 5th AFIR International Colloquium 1 ( 1995 ): 429-453.
Cairns, A.J.G. “Continuous-Time Stochastic Pension Funding Modelling, ” Proceedings of the 6th AFIR International Colloquium 1 ( 1996 ): 609-624.
Cairns, A.J.G. “Some Notes on The Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time,” ASTIN Bulletin 30-1 (2000): 19-55.
Chang, S.C. “Optimal Pension Funding Through Dynamic Simulations: the Case of Taiwan Public Employees Retirement System,” Insurance: Mathematics and Economics 24 ( 1999 ): 187-199.
Chang, S.C., “Stochastic Analysis of the Solvency Risk for TAIPERS Using Simulation-based Forecast Model,” Singapore International Insurance and Actuarial Journal 3-1 ( 1999 ): 65-81.
Chang, S.C. “Realistic Pension Funding : A Stochastic Approach,” Journal of Actuarial Practice 8 ( 2000 ): 5-42.

Chang, S.C., Tsai, C.H., Tien, C.J., and Tu, C.Y. ”Dynamic Funding and Investment Strategy for Defined Benefit Pension Schemes: A Model Incorporating Asset-Liability Matching Criteria.” Journal of Actuarial Practice 10 ( 2002 ): 131-154.
Haberman, S. “Pension Funding With Time Delays : A Stochastic Approach,.” Insurance: Mathematics and Economics 11 ( 1992 ): 179-189.
Haberman, S. “Pension Funding with Time Delays and Autoregressive Rates of Investment Return.” Insurance: Mathematics and Economics 13 ( 1993 ): 45-56.
Haberman, S. “Autoregressive Rates of Return and the Variability of Pension Contributions and Fund Levels for a Defined Benefit Pension Scheme.” Insurance: Mathematics and Economics 14 ( 1994 ): 219-240.
Haberman, S. and Sung, J.H. “Dynamic Approaches to Pension Funding.” Insurance: Mathematics and Economics 15 ( 1994 ): 151-162.
Haberman, S. and Wong, L.Y. “Moving Average Rates of Return and the Variability of Pension Contributions and Fund Levels for a Defined Benefit Pension Scheme,” Insurance : Mathematics and Economics 20 ( 1997 ): 115-135.
Josa-Fombellida R, and Rincon-Zapatero JP. “Minimization of Risks in Pension Funding by Means of Contribution and Portfolio Selection.” Insurance: Mathematics and Economics 29 ( 2001):35–45.
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Karatzas, I., Lehoczky, J.P., Sethi, S.P., and Shreve, S.E. “Explicit Solution of a General Consumption/Investment Problem.” Mathematics of Operations Research 11 ( 1986 ): 262-292.
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O'Brien, T. “A Stochastic-Dynamic Approach to Pension Funding.” Insurance: Mathematics and Economics 5 ( 1986 ):141-146.
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中文部分:
公務人員退撫基金第四次精算報告
網頁部分:
勞工保險局全球資訊網 http://www.bli.gov.tw/
公務人員退撫基金 http://www.fund.gov.tw/mp.asp?mp=1

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