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    題名: 動態規劃數值解 ：退休後資產配置
    Dynamic programming numerical solution: post retirement asset allocation
    作者: 蔡明諺
    Tsai, Ming Yen
    貢獻者: 黃泓智
    Huang, Hong Chih
    蔡明諺
    Tsai, Ming Yen
    關鍵詞: 資產配置
    動態規劃
    數值解
    二次損失函數
    破產機率
    Asset Allocation
    Dynamic Programming
    Numerical Solution
    Quadratic Loss Function
    ruin probability
    日期: 2009
    上傳時間: 2010-12-08 16:51:01 (UTC+8)
    摘要: 動態規劃的問題並不一定都存在封閉解(closed form solution)，即使存在，其過程往往也相當繁雜。本研究擬以 Gerrard & Haberman (2004) 的模型為基礎，並使用逼近動態規劃理論解的數值方法來求解，此方法參考自黃迪揚(2009)，其研究探討在有無封閉解的動態規劃下，使用此數值方法求解可以得到
    逼近解。本篇嘗試延伸其方法，針對不同類型的限制，做更多不同的變化。Gerrard & Haberman (2004)推導出退休後投資於風險性資產與無風險性資產之最適投資策略封閉解， 本研究欲將模型投資之兩資產衍生至三資產，分別投資在高風險資產、中風險資產與無風險資產，實際市場狀況下禁止買空賣空的情況與風險趨避程度限制資產投資比例所造成的影響。並探討兩資產與三資產下的投資結果，並加入不同的目標函數:使用控制變異數的限制式來降低破產機率、控制帳戶差異部位讓投資更具效率性。雖然加入這些限制式會導致目標函
    數過於複雜，但是用此數值方法還是可以得出逼近解。
    Dynamic Programming’s solution is not always a closed form. If it do exist, the solution of progress may be too complicated. Our research is based on the investing model in Gerrard & Haberman (2004), using the numerical solution by Huang (2009) to solve the dynamic programming problem. In his research, he found out that whether dynamic programming problem has the closed form, using the numerical solution to solve the problems, which could get similar result. So in our research, we try to use this solution to solve more complicate problems.
    Gerrard & Haberman (2004) derived the closed form solution of optimal investing strategy in post retirement investment plan, investing in risky asset and riskless asset. In this research we try to invest in three assets, investing in high risk asset, middle risk asset and riskless asset. Forbidden short buying and short selling, how risk attitude affect investment behavior in risky asset and riskless asset. We also observe the numerical result of 2 asset and 3 asset, using different objective functions : using variance control to avoid ruin risk, consideration the distance between objective account and actual account to improve investment effective. Although using these restricts may increase the complication of objective functions, but we can use this numerical solution to get the approximating solution.
    參考文獻: 1. Bacinello, A.R., 1988. "A stochastic simulation procedure for pension scheme". Insurance: Mathematics and Economics, vol.7, 153–161.
    2. Blake, D., Cairns, A. J. G. and Dowd, K., 2001. "Pensionmetrics： Stochastic pension plan design and value-at-risk during the accumulation phase". Insurance： Mathematics and Economics, vol.29, 187-215
    3. Blake, D., Cairns, A. J. G. and Dowd, K., 2003. "Pensionmetrics 2： Stochastic pension plan design during the distribution phase". Insurance： Mathematics and Economics, vol.33, 29-47
    4. Bordley, R., Li Calzi, M., 2000. "Decision analysis using targets instead of utility functions". Decisions in Economics and Finance, vol.23, 53-74.
    5. Browne, S., 1995. "Optimal investment policies for a firm with a random risk process： exponential utility and minimizing the probability of ruin". Mathematics of Operations Research, vol. 20, 937-958.
    6. Chang, S.C., 1999. "Optimal Pension Funding Through Dynamic Simulations： the Case of Taiwan Public Employees Retirement System". Insurance： Mathematics and Economics, vol.24, 187-199.
    7. Davidoff, T., Brown, J.R., Diamond, P.A., 2005. "Annuities and individual welfare". American Economic Review, vol.95, 1573-1590.
    8. Delong, Ł., 2005. "Optimal investment strategy for a non-life insurance company： quadratic loss". Appl. Math. (Warsaw), vol.32, 263-277.
    9. Delong, Ł., Gerrard, R., Haberman, S., 2008. "Mean-variance optimization problems for an accumulation phase in a defined benefit plan". Insurance： Mathematics and Economics, vol.35, 321-342.
    10. Gerrard, R., Haberman, S., Vigna, E., 2004. "Optimal investment choices post-retirement in a defined contribution pension scheme". Insurance： Mathematics and Economics, vol. 35, 321-342
    11. Haberman, S., Sung, J.H., 1994. "Dynamic Approaches to Pension Funding". Insurance： Mathematics and Economics, vol.15, 151-162
    12. Haberman, S., Vigna, E., 2002. "Optimal Investment Strategies and risk measures in defined contribution pension schemes". Insurance： Mathematics and Economics, vol.31, 35-69
    13. He, L., Liang, Z., 2009. "Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs". Insurance： Mathematics and Economics, vol.44, 88-94
    14. Horneff, W. J., Maurer, R. H., Mitchell, O. S., Dus, I., 2008. "Following the rules： Integrating asset allocation and annuitization in retirement portfolios". Insurance： Mathematics and Economics, vol.42, 396-408
    15. Horneff, W. J., Maurer, R. H., Stamos, M. Z., 2008. "Optimal gradual annutization： Quantifying the costs of switching to annuities". The Journal of Risk and Insurance, vol.75, 1019-1038.
    16. Huang, H. C., Cairns, A. J. G., 2006. "On the control of defined-benefit pension plans". Insurance： Mathematics and Econmics, vol. 38, 2006, 113-131.
    17. Kahneman, D., Tversky, A., 1979. "Prospect theory： an analysis of decision under risk". Econometrica, vol.47, 263-291.
    18. Orszag, J.M., 2000. "The annuities： the problem". In： Presented at the NAPF Annual Conference, May 11-12, 2000.
    19. Polyak, I., 2005. "New Advice to Retirees： Spend More at First, Cut Back Later". New York Times.
    20. Raymar, S.B. & M.J. Zwecher., 1997. "Monte Carlo Estimation of American Call Option on the Maximum of Several Assets". Journal of Derivatives, vol.5, 7-24
    21. Vigna, E., and Haberman, S., 2001. "Optimal Investment Strategy for defined contribution pension schemes". Insurance： Mathematics and Economics, vol.28, 233-262
    22. Winklevoss, H.E., 1982. "Plasm: pension liability and asset simulation model". Journal of Finance XXXVII (2) 585-594.
    23. 黃迪揚，2009年 "最適資產配置--動態規劃問題之數值解"，國立政治大學風險管理與保險學系碩士論文。
    描述: 碩士
    國立政治大學
    風險管理與保險研究所
    97358023
    98
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0973580231
    資料類型: thesis
    顯示於類別:[風險管理與保險學系] 學位論文

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