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    題名: 多期最適資產配置：一般化最小平方法之應用
    作者: 劉家銓
    貢獻者: 黃泓智
    謝明華


    劉家銓
    關鍵詞: 資產負債管理
    一般化最小平方法
    多期最適投資
    Asset liability matching
    generalized least square (GLS)
    multi-period approach
    日期: 2005
    上傳時間: 2009-09-18
    摘要: 本文主要是針對保險業及退休基金的資產負債管理議題為研究重心，延續Huang (2004)的研究，其研究是以理論求解的方式求出多期最適資產配置的唯一解，而其研究也衍生出兩個議題：首先是文中允許資產買賣空;再者其模型僅解決單期挹注資金的問題，而不考慮多期挹注資金。但這對於實際市場操作上會有一些的問題。因此本文延續了其研究，希望解決這兩個議題，讓模型更能解出一般化的資產負債管理問題。
    本文所選擇的投資的標的是以一般退休基金與保險業所採用，分別是短債(short-term bonds)、永續債卷(consols)、指數連結型債券(index-linked gilts(ILG))、股票(equity)為四種投資標的，以蒙地卡羅模型模擬出4000組Wilkie 投資模型(1995)下的四種標的年報酬率以及負債年成長率，利用這些預期的模擬值找出最適的投資比例以及應該挹注的金額。而本文主要將問題化為決策變數的二次函數，並以一般化最小平方法(generalized least square,GLS)來求出決策變數，而用此方法最大的優點在於一般化最小平方法具有唯一解，且在利用軟體求解的速度相當快，因此是非常有效率的。本文探討的問題可以分成兩個部分。我們首先討論「單期挹注資金」的問題，只考慮在期初挹注資金。接著我們考慮「多期挹注資金」的問題，是在計畫期間內能將資金分成多期投入。兩者都能將目標函數化為最小平方的形式，因此本文除了找出合理的資產配置以及解決多期挹注資金的問題之外，也將重點著重於找一個能快速且精準的方法來解決資產配置的問題。
    This paper deals with the insurance and pension asset liability management issue. Huang (2004) derives a theoretical close solution of multi-period asset allocation. However, there are two further problems in his paper. First, short selling is allowable. Second, multi-period investing is not acceptable. These two restrictions sometimes are big problems in practice. This paper extends his paper and releases these two restrictions. In other words, we intend to find a solution of multi-period asset allocation so that we can invest money and change proportion of investment in each period without problems of short selling.
    In this paper, we use the standard asset classes used by pension or insurance funds such as short-term bonds, consols, index-linked gilts and equities. We generate thousand times of Monte Caro simulations of Wilkie investment model (1995) to predict future asset returns. Furthermore, in order to improve time-efficiency and accuracy, we derive a quadratic objective function and obtain a unique solution using sequential quadratic programming.
    參考文獻: 1. Berketi, A.,(1998),“Allowing for insurance companies’ liabilities in mean-variance models.” Ph.D. Thesis, Heriot-Watt University, Edinburgh
    2. Boyle, P. and Yang H.(1997). “Asset Allocation with Time Variation in Expected Returns.” Insurance: Mathematics and Economic 21: 201-218
    3. Brennan,M.J., and Schwartz,E.S., and Lagnado, R., (1997), “Strategic Asset Allocation”, Journal of Economic Dynamics and Control, 21: 1377-1403
    4. Brianton, G.,(1997)“Risk Management and Financial Derivatives,” 431-469.
    5. Cairns,A.J.,(1999). “A multifactor model for the term structure and inflation for long-term risk management with an extension to the equities market.“ Proceedings of the 9th AFIR Colloquium, Tokyo, (3):93-113.
    6. Cariño, and David,R., and Andrew,L., and Turner, “Multiperiod asset allocation with derivative assets”, In: Ziemba W.T., Mulvey, J.M., eds.,Worldwide Asset and Liability Modeling, Cambridge University Press, 182-204
    7. 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.
    8. Chopra, V.K., and Ziemba,W.T., (1993) “The effect of errors in means, variances, and covariances on optimal portfolio choice”, Journal of Portfolio Management 19.
    9. Edesess,M and Hambrecht,G.A., (1980),”Scenario Forecasting；Necessity,not choice”. Financial Analyst Journal
    10. Gill, P.E., and Murray,W., and Wright,M.H., (1981) “Practical Optimization. Academic Press.” section 5.3.2 and 5.3.3
    11. Haberman,S., and Sung,J.H., (1994).“Dynamic Approach to Pension Funding.” Insurance: Mathematics and Economics, 15: 151-162.
    12. Hardy,M.R.,(1993). “Stochastic simulation in life office solvency.” Journal of the Institute of Actuaries, (120):131-152
    13. Huang,H.C.,（2000）：“ Stochastic Modeling and Control of Pension Plans,” PH.D. Thesis, Heriot-Watt University
    14. Huang,H.C.,（2004).”Optimal Asset Allocation: A Multi-Period Matching of Assets to Liabilities in a Discrete Model”, submitted to Insurance: Mathematics and Economics
    15. Koskosidis,Y.A., and Duarte,A.M., (1997), “A Scenario-Based Approach to Active Asset Allocation”, The Journal of Portfolio Management, Winter.
    16. Macdonald,A.,(1994), “A Stochastic evaluation of solvency valuations for life officies”. PH.D. Thesis, Heriot-Watt University
    17. Markowitz, and Harry, （1952）.“Portfolio Selection”. Journal of Finance ,pp.77-91.
    18. Sherris,（1992）,”Portfolio Selection and Matching :A synthesis”. J.I.A.119,I,pp.87-105.
    19. Vigna,E., and Haberman,S.,（2001）.” Optimal investment strategy for defined contribution pension schemes” Insurance: Mathematics and Economics, 28: 233-262
    20. 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
    21. Wilkie, A. D., (1986), “A Stochastic Investment Model for Actuarial Use”, Transactions of the Faculty of Actuaries, 39, pp.341-381.
    22. Wilkie, A.D.,（1995）：“ More on a stochastic asset model for actuarial use,” British Actuarial Journal 1, 777-964
    23. Wise, A.J., （1984a）”A theoretical analysis of the matching of assets to liabilities.” Journal of Institute of Actuaries,111（Part II）：375-402
    24. Wise, A.J., （1984b）”The matching of assets to liabilities.” Journal of the Institute of Actuaries,111(Part II)：445-501
    25. Wise, A.J.,（1987a） “Matching and Portfolio Selection:Part 1 “Journal of Institute of Actuaries,114, 113-133
    26. Wise, A.J.,（1987b） “Matching and Portfolio Selection:Part 2” Journal of Institute of Actuaries,114, 551-568
    27. Wright, I.D.,(1998) “Traditional pension fund valuation in a stochastic asset and liability environment”. British Actuarial Journal, 4(IV):865-901
    28. Yakoubov, Y., and Teeger,M., and Duval, D.,（1999）：“ A stochastic investment model for asset and liability management,” In proceedings of the 9th International AFIR Colloquium, Tokyo, August,1999,（Joint ASTIN/AFIR volume）,237-266
    29. 鄧益俗，2002。多期基金之最適資產配置：擬似動態規劃之應用，國立政治大學風險管理與保險研究所未出版碩士論文。
    描述: 碩士
    國立政治大學
    風險管理與保險研究所
    92358023
    94
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0923580231
    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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