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題名 均值-變異數準則下之最適基金管理策略
Optimal Fund Management under the Mean-Variance Approach作者 李永琮
Lee, Yung Tsung貢獻者 黃泓智
Huang, Hong Chih
李永琮
Lee, Yung Tsung關鍵詞 資產配置
保單組合
確定提撥
Lee-Carter模型
時間修正
Asset allocation
policy portfolio
DC pension plan
Lee-Carter mode
Time adjustment
Anticipative model
Adaptive model日期 2009 上傳時間 9-May-2016 11:51:49 (UTC+8) 摘要 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.參考文獻 Battocchio, P., Menoncin, F., 2004. Optimal pension management in a stochastic framework. Insurance: Mathematics and Economics 34, 79-95.Be´dard, D., 1999. Stochastic pension funding: proportional control and bilinear processes. ASTIN Bulletin 29, 271-293.Bedard, D., Dufresne, D., 2001. Pension fund with moving average rates of return. Scandinavian Actuarial Journal 1, 1-17.Blake, D., Cairns, A. J. G., Dowd, K., 2001. Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase. Insurance: Mathematics and Economics 29, 187-215.Boulier, J.F., Huang, S., Taillard, G., 2001. Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund. Insurance: Mathematics and Economics 28, 173–189.Cairns, A. J. G., 2000. Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time. ASTIN Bulletin 30, 19–55.Cairns, A. J. G., Blake, D., Dowd, K., 2006. A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance 73, 687-718. Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A., Balevich, I., 2007. A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. Working paper.Cairns, A.J.G., Blake, D., Dowd, K., 2008. Modelling and management of mortality risk: a review. To appear in Scandinavian Actuarial Journal.Cairns, A.J.G., Parker, G., 1997. Stochastic pension fund modeling. Insurance: Mathematics and Economics 21, 43-79.Campbell, J.Y., Viceira, L.M., 2002. Strategic Asset Allocation: Portfolio Choice for Long-term Investors. Oxford University Press, Oxford.Chang, S.C., Tzeng, L.T., Miao, J.C.Y., 2003. Pension funds incorporating downside risk. Insurance: Mathematics and Economics 32, 217–228.Chiu, M. C., Li, D., 2006. Asset and liability management under a continuous-time mean–variance optimization framework. Insurance: Mathematics and Economics 39, 330–355.CMI Committee, 1999. Standard tables of mortality based on the 1991-1994 experiences. Continuous Mortality Reports 17, Institute and Faculty of Actuaries, 1-227.Coppola, M., Lorenzo, E. D., Sibillo, M., 2003. Stochastic analysis in life office management: applications to large annuity portfolios. Applied Stochastic Models in Business and Industry 19. 31-42.Courakis, A. S., 1974. Clearing bank asset choice behaviour: A mean-variance treatment. Oxford Bulletin of Economics and Statistics 36, 173-201.Debicka, J., 2003. Moments of the cash value of future payment streams arising from life insurance contracts. Insurance: Mathematics and Economics 33, 533-550.Deelstra, G., Grasselli, M., Koehl, P.F., 2003. Optimal investment strategies in the presence of a minimum guarantee. Insurance: Mathematics and Economics 33, 189–207.Delong, L., Gerrard, R., Haberman, S., 2008. Mean–variance optimization problems for an accumulation phase in a defined benefit plan. Insurance: Mathematics and Economics 42, 107–118.Devolder, P., Bosch, P.M., Dominguez, F.I., 2003. Stochastic optimal control of annuity contracts. Insurance: Mathematics and Economics 33, 227-238.Dufresne, D., 1988. Moments of pension fund contributions and fund level when rates of return are random. Journal of the Institute of Actuaries 115, 535-544.Dufresne, D., 1989. Stability of pension systems when rates of return are random. Insurance: Mathematics and Economics 8, 71-76.Dufresne, D., 2007. Stochastic life annuities. North American Actuarial Journal 11, 136-157.Emms, P., Haberman, S., 2007. Asymptotic and numerical analysis of the optimal investment strategy for an insurer. Insurance: Mathematics and Economics 40, 113–134.Gerrard, R., Haberman, S., Vigna, E., 2004. Optimal investment choices post-retirement in a defined contribution pension scheme. Insurance: Mathematics and Economics 35, 321–342.Gerber, H. U., Shiu, E. S. W., 2003. Geometric Brownian motion models for asset and liabilities: From pension funding to optimal dividends. North American Actuarial Journal 7, 37-56.Haberman, S., 1994. Autoregressive rates of return and the variability of pension contributions and fund levels for a defined benefit pension scheme. Insurance: Mathematics and Economics 14, 219-240.Haberman, S., 1997. Stochastic investment return and contribution rate in a defined benefit pension scheme. Insurance: Mathematics and Economics 19, 127-139.Haberman, S., Butt, Z., Megaloudi, C., 2000. Contribution and solvency risk in a defined benefit pension scheme. Insurance: Mathematics and Economics 27, 237-259.Haberman, S., Sung, J. H., 1994. Dynamic Approach to Pension Funding. Insurance: Mathematics and Economics 15, 151-162.Haberman, S., Vigna, E., 2002. Optimal investment strategy and risk measures in defined contribution pension schemes. Insurance: Mathematics and Economics 31, 35-69.Hainaut, D., Devolder, P., 2007, Management of a pension fund under mortality and financial risks. Insurance: Mathematics and Economics 41, 134-155.Hoedemakers, T., Darkiewicz, G., Goovaerts, M., 2005. Approximations for life annuity contracts in a stochastic financial environment. Insurance: Mathematics and Economics 37, 239-269.Huang, H. C., Cairns, A. J. G., 2006. On the control of defined-benefit pension plans. Insurance: Mathematics and Economics 38, 113-131.Hurlimann, W., 2002. On the accumulated aggregate surplus of a life portfolio. Insurance: Mathematics and Economics 30, 27-35.Janssen, F., Kunst, A., 2007. The choice among past trends as a basis for the prediction of future trends in old-age mortality. Population Studies 61, 315-326.Kahane, Y., Nye, D., 1975. A portfolio approach to the property-liability insurance industry. Journal of Risk and Insurance 42, 579-598.Lai, S.L., Frees, E., 1995. Examining changes in reserves using stochastic interest models. Journal of Risk and Insurance 62, 535–574.Lee, R., 2000. The Lee-Carter method for forecasting mortality, with various extensions and applications. North American Actuarial Journal 4, 80-93.Lee, R. D., Carter, L. R., 1992. Modeling and forecasting U.S. mortality. Journal of the American Statistical Association 87, 659-675.Lin, Y., Cox, S. H., 2005. Securitization of mortality risks in life annuities. Journal of Risk and Insurance 72, 227-252.Lintner, J., 1965. The valuation of risky assets and the selection of risky investment in stock portfolios and capital budgets. Review of Economics and Statistics 47, 13-37.M. A. H. Dempster (ed.): Stochastic Programming. Academic Press, London, 1980.Mandl, P., Mazurova, L., 1996. Harmonic analysis of pension funding methods. Insurance: Mathematics and Economics 14, 127-139.Marceau, E. Gaillardetz, P., 1999. On Life Insurance Reserves in a Stochastic Mortality and Interest Rates Environment. Insurance: Mathematics and Economics 25, 261-280.Markowitz, H., 1952. Portfolio selection. Journal of Finance 7, 77-91.Markowitz, H., 1959. Portfolio selection: Efficient diversification of investments. New York: Wiley.Merton, R. C., 1971. Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373-413.Mossin, J., 1966. Equilibrium in a capital asset market. Econometrica 34, 768-783.Parkin, M., 1970. Discounted house portfolio and debt selection. Review of Econoic Studies 37, 469-497.Perry, D., Stadje, W., Yosef, R., 2003. Annuities with controlled random interest rates. Insurance: Mathematics and Economics 32, 245-253.Ross, S., 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13, 341-360.Sharpe, W. F., 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19, 425-442.Sharpe, W. F., Tint, I. G., 1990. Liabilities: A new approach. Journal of Portfolio Management, Winter, 5-10.Sherris, M., 1992. Portfolio Selection and Matching: A Synthesis. Journal of the Institute of Actuaries 119, 87-105.Sherris, M., 2006. Solvency, capital allocation, and fair rate of return in insurance. The Journal of Risk and Insurance 73, 71-96.Tobin, J., 1958. Liquidity preference as behavior towards risk. Review of Economic Studies 25, 68-85.Vigna, E., Haberman, S., 2001. Optimal investment strategy for defined contribution pension schemes. Insurance: Mathematics and Economics 28, 233-262.Wang, N., Gerrard, R., Haberman, S., 2004. The premium and the risk of a life policy in the presence of interest rate fluctuations. Insurance: Mathematics and Economics 35, 537-551.Wang, Z., Xia, J., Zhang, L., 2007. Optimal investment for an insurer: The martingale approach. Insurance: Mathematics and Economics 40, 322–334.Wilkie, A. D., 1995. More on a stochastic asset model for actuarial use. British Actuarial Journal 1, 777-964.Wilkie, A. D., 1985. Portfolio Selection in the Presence of Fixed Liabilities: A Comment on The Matching of Assets to Liabilities. Journal of Institute of Actuaries 112, 229-277.Wilmoth, J. R., 1993. Computational methods for fitting and extrapolating the Lee-Carter model of mortality change. Technical report, Berkeley, University of California.Wilmoth, J. R., 2005. Overview and discussion of the social security mortality projections. Working paper, department of demography, Berkeley, university of California.Wise, A. J., 1984a. A theoretical analysis of the matching of assets to liabilities. Journal of Institute of Actuaries 111, Part II, 375-402.Wise, A. J., 1984b. The matching of assets to liabilities. Journal of the Institute of Actuaries 111, Part II, 445-501.Wise, A. J., 1987a. Matching and Portfolio Selection: Part 1. Journal of Institute of Actuaries 114, 113-133.Wise, A. J., 1987b. Matching and Portfolio Selection: Part 2. Journal of Institute of Actuaries 114, 551-568.Zaks, A., 2001. Annuities under random rates of interest. Insurance: Mathematics and Economics 28, 1-11. 描述 博士
國立政治大學
風險管理與保險研究所
93358504資料來源 http://thesis.lib.nccu.edu.tw/record/#G0933585041 資料類型 thesis dc.contributor.advisor 黃泓智 zh_TW dc.contributor.advisor Huang, Hong Chih en_US dc.contributor.author (Authors) 李永琮 zh_TW dc.contributor.author (Authors) Lee, Yung Tsung en_US dc.creator (作者) 李永琮 zh_TW dc.creator (作者) Lee, Yung Tsung en_US dc.date (日期) 2009 en_US dc.date.accessioned 9-May-2016 11:51:49 (UTC+8) - dc.date.available 9-May-2016 11:51:49 (UTC+8) - dc.date.issued (上傳時間) 9-May-2016 11:51:49 (UTC+8) - dc.identifier (Other Identifiers) G0933585041 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/94776 - dc.description (描述) 博士 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) 93358504 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents Chapter 1. Introduction 1 Chapter 2. The asset return model and the moments 5 2.1. Moments of a general accumulated fund 5 2.2. The asset return model 6 2.3. The moments of the accumulation factor 72.4. Adding a foreign stocks 9 2.5 A dynamic labor income process 12 Chapter 3. Optimal Asset Allocation for A General Portfolio of Life Insurance Policies 17 3.1. Introduction 17 3.2. Model Setting 193.3. Optimal Asset Allocation 223.4. Sensitivity Analysis 283.5. Considering a foreign stocks 36 3.6. Conclusion 39 Chapter 4. Optimal Asset Allocation Incorporating Longevity Risk in Defined Contribution Pension Plans 414.1. Introduction 414.2. Mortality trends over time 434.3. Model Setting 534.4. Numerical results 554.5. Considering the dynamic of labor income 664.6. Conclusion 71 Chapter 5. Comparative Efficiency- Anticipative Model versus Adaptive Model 735.1. Introduction 73 5.2. A brief review of Vigna and Haberman (2001) 755.3. Numerical results 815.4. Conclusion 97 Chapter 6. Conclusions 99 Appendix Appendix A 101Appendix B 110Appendix C 113Appendix D 115Appendix E 118Appendix F 123Appendix G 124Appendix H 125Appendix I 132 References 133 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0933585041 en_US dc.subject (關鍵詞) 資產配置 zh_TW dc.subject (關鍵詞) 保單組合 zh_TW dc.subject (關鍵詞) 確定提撥 zh_TW dc.subject (關鍵詞) Lee-Carter模型 zh_TW dc.subject (關鍵詞) 時間修正 zh_TW dc.subject (關鍵詞) Asset allocation en_US dc.subject (關鍵詞) policy portfolio en_US dc.subject (關鍵詞) DC pension plan en_US dc.subject (關鍵詞) Lee-Carter mode en_US dc.subject (關鍵詞) Time adjustment en_US dc.subject (關鍵詞) Anticipative model en_US dc.subject (關鍵詞) Adaptive model en_US dc.title (題名) 均值-變異數準則下之最適基金管理策略 zh_TW dc.title (題名) Optimal Fund Management under the Mean-Variance Approach en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Battocchio, P., Menoncin, F., 2004. Optimal pension management in a stochastic framework. Insurance: Mathematics and Economics 34, 79-95.Be´dard, D., 1999. Stochastic pension funding: proportional control and bilinear processes. ASTIN Bulletin 29, 271-293.Bedard, D., Dufresne, D., 2001. Pension fund with moving average rates of return. Scandinavian Actuarial Journal 1, 1-17.Blake, D., Cairns, A. J. G., Dowd, K., 2001. Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase. Insurance: Mathematics and Economics 29, 187-215.Boulier, J.F., Huang, S., Taillard, G., 2001. Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund. Insurance: Mathematics and Economics 28, 173–189.Cairns, A. J. G., 2000. Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time. ASTIN Bulletin 30, 19–55.Cairns, A. J. G., Blake, D., Dowd, K., 2006. A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance 73, 687-718. Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A., Balevich, I., 2007. A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. Working paper.Cairns, A.J.G., Blake, D., Dowd, K., 2008. Modelling and management of mortality risk: a review. To appear in Scandinavian Actuarial Journal.Cairns, A.J.G., Parker, G., 1997. Stochastic pension fund modeling. Insurance: Mathematics and Economics 21, 43-79.Campbell, J.Y., Viceira, L.M., 2002. Strategic Asset Allocation: Portfolio Choice for Long-term Investors. Oxford University Press, Oxford.Chang, S.C., Tzeng, L.T., Miao, J.C.Y., 2003. Pension funds incorporating downside risk. Insurance: Mathematics and Economics 32, 217–228.Chiu, M. C., Li, D., 2006. Asset and liability management under a continuous-time mean–variance optimization framework. Insurance: Mathematics and Economics 39, 330–355.CMI Committee, 1999. Standard tables of mortality based on the 1991-1994 experiences. Continuous Mortality Reports 17, Institute and Faculty of Actuaries, 1-227.Coppola, M., Lorenzo, E. D., Sibillo, M., 2003. Stochastic analysis in life office management: applications to large annuity portfolios. Applied Stochastic Models in Business and Industry 19. 31-42.Courakis, A. S., 1974. Clearing bank asset choice behaviour: A mean-variance treatment. Oxford Bulletin of Economics and Statistics 36, 173-201.Debicka, J., 2003. Moments of the cash value of future payment streams arising from life insurance contracts. Insurance: Mathematics and Economics 33, 533-550.Deelstra, G., Grasselli, M., Koehl, P.F., 2003. Optimal investment strategies in the presence of a minimum guarantee. Insurance: Mathematics and Economics 33, 189–207.Delong, L., Gerrard, R., Haberman, S., 2008. Mean–variance optimization problems for an accumulation phase in a defined benefit plan. 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