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題名 確定給付退休金計畫於總和精算成本法之最適控制
Optimal Control of the Defined Benefit Pension Schemes under Aggregate Actuarial Cost Method
作者 葉倩妏
Yeh,chien wen
貢獻者 張士傑
葉倩妏
Yeh,chien wen
關鍵詞 最適提撥
資產配置
總和精算成本法
optimal contribution
asset allocation
aggregate actuarial cost method
日期 2009
上傳時間 8-十二月-2010 01:57:19 (UTC+8)
摘要 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.
參考文獻 英文部分:
Anderson, A.W. Pension Mathematics for Actuaries, 3rd ed. Winsted, Conn.: Actex Publication, 2006.
Björk, T. Arbitrage Theory in Continuous Time, 3rd ed. Oxford University Press, 2009.
Campbell, J.Y. and Viceira, L.M. Strategic Asset Allocation, 2nd ed. Oxford University Press, 2003.
Boyle, P. and Yang, H. “Asset Allocation with Time Variation in Expected Returns.” Insurance : Mathematics and Economics 21 ( 1997 ): 201-218.
Bellman, R. Dynamic Programming, Princeton, N.J. : Princeton University Press, 1957.
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.
Brennan, M.J., Schwartz, E.S. “An Equilibrium Model of Bond Pricing and A Test of Market Efficiency.” Journal of Financial and Quantitative Analysis 17 ( 1982 ): 301-329.
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.
Brennan, M.J., Schwartz, E.S. and Lagnado, R. “Strategic Asset Allocation,” Journal of Economics, Dynamics and Control 21 ( 1997 ): 1377-1403.
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.
Josa-Fombellida, R., and Rincon-Zapatero, J.P. “Optimal risk management in defined benefit stochastic pension funds.” Insurance: Mathematics and Economics 34 ( 2004 ): 489–503.
Josa-Fombellida, R., and Rincon-Zapatero, J.P. “Optimal investment decisions with a liability: The case of defined benefit pension plans.” Insurance: Mathematics and Economics 39 ( 2006 ): 81–98.
Josa-Fombellida, R., and Rincon-Zapatero, J.P. “Funding and Investment Decisions in a Stochastic Defined Benefit Pension Plan with Several Levels of Labor-Income Earnings.” Computers and Operations Research 35 ( 2008 ): 47–63.
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.
Merton, R.C. “Optimal Consumption and Portfolio Rules in a Continuous Time Model.” Journal of Economic Theory 3 ( 1971 ): 373-413.
Merton, R.C. Continuous-Time Finance, Oxford, England: Blackwell, 1990.
O`Brien, T. “A Stochastic-Dynamic Approach to Pension Funding.” Insurance: Mathematics and Economics 5 ( 1986 ):141-146.
O`Brien, T. “A Two-Parameter Family of Pension Contribution Functions and Stochastic Optimization.” Insurance: Mathematics and Economics 6 ( 1987 ):129-134.
Owadally, M.L. and Haberman, S. “Pension Fund Dynamics and Gains/ Losses Due to Random Rates of Investment Return,” North American Actuarial Journal 3-3 ( 1999 ):105-117.
Samuelson, P. “Lifetime Portfolio Selection by Dynamic Stochastic Programming.” Review of Economics and Statistics ( 1969 ): 239-246.
Taylor, G. “Stochastic control of funding systems.” Insurance: Mathematics and Economics 30 ( 2002 ): 323–350.
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
描述 碩士
國立政治大學
風險管理與保險研究所
97358021
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097358021
資料類型 thesis
dc.contributor.advisor 張士傑zh_TW
dc.contributor.author (作者) 葉倩妏zh_TW
dc.contributor.author (作者) Yeh,chien wenen_US
dc.creator (作者) 葉倩妏zh_TW
dc.creator (作者) Yeh,chien wenen_US
dc.date (日期) 2009en_US
dc.date.accessioned 8-十二月-2010 01:57:19 (UTC+8)-
dc.date.available 8-十二月-2010 01:57:19 (UTC+8)-
dc.date.issued (上傳時間) 8-十二月-2010 01:57:19 (UTC+8)-
dc.identifier (其他 識別碼) G0097358021en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49033-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險研究所zh_TW
dc.description (描述) 97358021zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) 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%。
zh_TW
dc.description.abstract (摘要) 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.
en_US
dc.description.tableofcontents 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
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097358021en_US
dc.subject (關鍵詞) 最適提撥zh_TW
dc.subject (關鍵詞) 資產配置zh_TW
dc.subject (關鍵詞) 總和精算成本法zh_TW
dc.subject (關鍵詞) optimal contributionen_US
dc.subject (關鍵詞) asset allocationen_US
dc.subject (關鍵詞) aggregate actuarial cost methoden_US
dc.title (題名) 確定給付退休金計畫於總和精算成本法之最適控制zh_TW
dc.title (題名) Optimal Control of the Defined Benefit Pension Schemes under Aggregate Actuarial Cost Methoden_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 英文部分:zh_TW
dc.relation.reference (參考文獻) Anderson, A.W. Pension Mathematics for Actuaries, 3rd ed. Winsted, Conn.: Actex Publication, 2006.zh_TW
dc.relation.reference (參考文獻) Björk, T. Arbitrage Theory in Continuous Time, 3rd ed. Oxford University Press, 2009.zh_TW
dc.relation.reference (參考文獻) Campbell, J.Y. and Viceira, L.M. Strategic Asset Allocation, 2nd ed. Oxford University Press, 2003.zh_TW
dc.relation.reference (參考文獻) Boyle, P. and Yang, H. “Asset Allocation with Time Variation in Expected Returns.” Insurance : Mathematics and Economics 21 ( 1997 ): 201-218.zh_TW
dc.relation.reference (參考文獻) Bellman, R. Dynamic Programming, Princeton, N.J. : Princeton University Press, 1957.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Brennan, M.J., Schwartz, E.S. “An Equilibrium Model of Bond Pricing and A Test of Market Efficiency.” Journal of Financial and Quantitative Analysis 17 ( 1982 ): 301-329.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Brennan, M.J., Schwartz, E.S. and Lagnado, R. “Strategic Asset Allocation,” Journal of Economics, Dynamics and Control 21 ( 1997 ): 1377-1403.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Cairns, A.J.G. “Continuous-Time Stochastic Pension Funding Modelling, ” Proceedings of the 6th AFIR International Colloquium 1 ( 1996 ): 609-624.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Chang, S.C. “Realistic Pension Funding : A Stochastic Approach,” Journal of Actuarial Practice 8 ( 2000 ): 5-42.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Haberman, S. “Pension Funding With Time Delays : A Stochastic Approach,.” Insurance: Mathematics and Economics 11 ( 1992 ): 179-189.zh_TW
dc.relation.reference (參考文獻) Haberman, S. “Pension Funding with Time Delays and Autoregressive Rates of Investment Return.” Insurance: Mathematics and Economics 13 ( 1993 ): 45-56.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Haberman, S. and Sung, J.H. “Dynamic Approaches to Pension Funding.” Insurance: Mathematics and Economics 15 ( 1994 ): 151-162.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Josa-Fombellida, R., and Rincon-Zapatero, J.P. “Optimal risk management in defined benefit stochastic pension funds.” Insurance: Mathematics and Economics 34 ( 2004 ): 489–503.zh_TW
dc.relation.reference (參考文獻) Josa-Fombellida, R., and Rincon-Zapatero, J.P. “Optimal investment decisions with a liability: The case of defined benefit pension plans.” Insurance: Mathematics and Economics 39 ( 2006 ): 81–98.zh_TW
dc.relation.reference (參考文獻) Josa-Fombellida, R., and Rincon-Zapatero, J.P. “Funding and Investment Decisions in a Stochastic Defined Benefit Pension Plan with Several Levels of Labor-Income Earnings.” Computers and Operations Research 35 ( 2008 ): 47–63.zh_TW
dc.relation.reference (參考文獻) 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.zh_TW
dc.relation.reference (參考文獻) Merton, R.C. “Optimal Consumption and Portfolio Rules in a Continuous Time Model.” Journal of Economic Theory 3 ( 1971 ): 373-413.zh_TW
dc.relation.reference (參考文獻) Merton, R.C. Continuous-Time Finance, Oxford, England: Blackwell, 1990.zh_TW
dc.relation.reference (參考文獻) O`Brien, T. “A Stochastic-Dynamic Approach to Pension Funding.” Insurance: Mathematics and Economics 5 ( 1986 ):141-146.zh_TW
dc.relation.reference (參考文獻) O`Brien, T. “A Two-Parameter Family of Pension Contribution Functions and Stochastic Optimization.” Insurance: Mathematics and Economics 6 ( 1987 ):129-134.zh_TW
dc.relation.reference (參考文獻) Owadally, M.L. and Haberman, S. “Pension Fund Dynamics and Gains/ Losses Due to Random Rates of Investment Return,” North American Actuarial Journal 3-3 ( 1999 ):105-117.zh_TW
dc.relation.reference (參考文獻) Samuelson, P. “Lifetime Portfolio Selection by Dynamic Stochastic Programming.” Review of Economics and Statistics ( 1969 ): 239-246.zh_TW
dc.relation.reference (參考文獻) Taylor, G. “Stochastic control of funding systems.” Insurance: Mathematics and Economics 30 ( 2002 ): 323–350.zh_TW
dc.relation.reference (參考文獻) 中文部分:zh_TW
dc.relation.reference (參考文獻) 公務人員退撫基金第四次精算報告zh_TW
dc.relation.reference (參考文獻) 網頁部分:zh_TW
dc.relation.reference (參考文獻) 勞工保險局全球資訊網 http://www.bli.gov.tw/zh_TW
dc.relation.reference (參考文獻) 公務人員退撫基金 http://www.fund.gov.tw/mp.asp?mp=1zh_TW