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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/49681


    Title: 最適資產配置-動態規劃問題之數值解
    Optimal asset allocation-the numerical solution of dynamic programming
    Authors: 黃迪揚
    Huang, Di Yang
    Contributors: 黃泓智
    Huang, Hong Chih
    黃迪揚
    Huang, Di Yang
    Keywords: 資產配置
    動態規劃
    數值解
    Asset Allocation
    Dynamic Programming
    Numerical Solution
    Date: 2008
    Issue Date: 2010-12-08 16:36:41 (UTC+8)
    Abstract: 動態規劃是一種專門用來解決最適化的數學方法，其觀念源自於Bellman (1962)，他提出了動態規劃的最佳原則，然而動態規劃問題不見得有封閉解(closed form solution)，即使其存在，求解過程往往也相當困難且複雜。Vigna & Haberman (2001)用動態規劃方式找出最佳的投資策略並分析確定提撥制(defined contribution)下的財務風險；本研究擬以Vigna & Haberman (2001)的模型為基礎，提出解決動態規劃問題的數值方法。

    Vigna & Haberman (2001)推導出確定提撥退休金制度下離散時間的最適投資策略封閉解，透過該模型，我們可以比較本研究所建議的方法與真正封閉解的差異，證實本研究所建議的方法的確可以提供動態規劃問題一個接近且有效率的數值解法。接著根據Yvonne C.(2002、2003)的抽樣方法，希望在進行模擬時，能找出模擬情境的特性並對這些情境進行抽樣，藉此減少情境數以增加電腦運算的效率。最後應用在Vigna & Haberman (2001)的修正模型以及Haberman & Vigna (2002)的模型上，說明了本研究所建議的數值方法也適用在各類型的動態規劃上，包含理論封閉解不存在以及求解非常複雜的問題。
    Reference: 1. Chang, S.C., (1999), "Optimal Pension Funding Through Dynamic Simulations: the Case of Taiwan Public Employees Retirement System." Insurance: Mathematics and Economics, 24, 187-199.
    2. Chryssoverghi and Bacopoulos, Discrete approximation of relaxed optimal control problems. Journal of Optimization Theory and Applications, 1990, 395-407
    3. C.-S. Huang, S. Wang and K.L. Teo, Solving Hamilton-Jacobi-Bellman equations by a modified method of characteristics. Nonlinear Analysis 40 (2000), 279-293.
    4. Haberman, S., and Sung, J.H., (1994), "Dynamic Approaches to Pension Funding" Insurance: Mathematics and Economics, 15, p151-162.
    5. Haberman, S., and Vigna, E., (2002), "Optimal Investment Strategies and risk measures in defined contribution pension schemes." Insurance mathematics and Economics, 31, p35-69.
    6. M. A. H. Dempster, (1980), "Stochastic programming " International Conference on Stochastic Programming, Oxford, 1974
    7. Markowitz, and Harry, （1952）.“Portfolio Selection”. Journal of Finance ,pp.77-91.
    8. M. G. Crandall and P.L. Lions, Two approximations of solutions of Hamilton-Jacobi equations. Mathematics of Computation 43 (1984), 1-19.
    9. Sherris,（1992）,”Portfolio Selection and Matching :A synthesis”. J.I.A.119,I,pp.87-105.
    10. S. Wang, F. Gao and K.L. Teo, An upwind finite-difference method for the approximation of viscosity solutions to Hamilton-Jacobi-Bellman equations. IMA J. Math. Control 17 (2000), 167-178.
    11. Vigna, E., and Haberman, S., (2001), "Optimal Investment Strategy for defined contribution pension schemes." Insurance mathematics and Economics, 28, p233-262.
    12. 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
    13. Wise, A.J., （1984a）”A theoretical analysis of the matching of assets to liabilities.” Journal of Institute of Actuaries,111（Part II）：375-402
    14. Wise, A.J., （1984b）”The matching of assets to liabilities.” Journal of the Institute of Actuaries,111(Part II)：445-501
    15. Wise, A.J.,（1987a） “Matching and Portfolio Selection:Part 1 “Journal of Institute of Actuaries,114, 113-133
    16. Wise, A.J.,（1987b） “Matching and Portfolio Selection:Part 2” Journal of Institute of Actuaries,114, 551-568
    17. Yvonne, C., (2002), "Efficient Stochastic Modeling For Large and Consolidated Insurance Business：Interest Rate Sampling Algorithms." North American Actuarial Journal, Vol.6 Iss. 3, p88-103.
    18. Yvonne, C., (2003), " Efficient Stochastic Modeling：From Scenario Sampling To Parametric Model Fitting Utilizing ASEM as an Exampling." International Professional Development Symposium Co-sponsored by Canadian Institute of Actuaries, Actuarial Foundation, and Society of Actuaries, Toronto, Canada.
    Description: 碩士
    國立政治大學
    風險管理與保險研究所
    96358021
    97
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0096358021
    Data Type: thesis
    Appears in Collections:[Department of Risk Management and Insurance] Theses

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