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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/60051


    Title: 附最低保證變額年金保險最適資產配置及準備金之研究
    A study of optimal asset allocation and reserve for variable annuities insurance with guaranteed minimum benefit
    Authors: 陳尚韋
    Contributors: 黃泓智
    李永崇
    陳尚韋
    Keywords: 附投資保證提領保險商品
    變額年金
    動態規劃求解
    冪次效用函數
    ARIMA-GARCH 模型
    GMWB
    Variable Annuities
    Dynamic Programming
    Power Utility Function
    ARIMA-GARCH model
    Date: 2010
    Issue Date: 2013-09-04 15:01:56 (UTC+8)
    Abstract: 附最低保證投資型保險商品的特色在於無論投資者的投資績效好壞，保險金額皆享有一最低投資保證，過去關於此類商品的研究皆假設標的資產為單一資產，或依固定比例之投資組合，並沒有考慮到投資人自行配置投資組合的效果，但大部分市售商品中，投資人可以自行配置投資標，此情況之下，保險公司如何衡量適當的保證成本即為一相當重要之課題。
    本研究假設投資人風險偏好服從冪次效用函數，並假設與保單所連結之投資標的有兩種資產，一為具有高風險高報酬的資產，另一為具有低風險低報酬之資產，在每個保單年度之初，投資人可以選擇配置在兩種資產之比例，我們運用黃迪揚(2009)所提出的動態規劃數值解之方法，計算出在考慮投資人自行配置資產之下，保證成本將會比固定比例之投資高出12個百分點。
    此外，為了瞭解在不同資產報酬率的模型之下，保證成本是否會有不一樣的結論，除了對數常態模型之外，我們假設高風險資產與低風險資產服從ARIMA-GARCH(Autoregressive Integrated Moving Average-Generalized Autoregressive Conditional Heteroscedastic )模型，並得到較高的保證成本。
    The main characteristic of variable annuities (VA) with minimum benefits is that the benefit will be guaranteed. Previous literatures assume a specific underling asset return process when considering the guaranteed cost of VA; but they do not consider the portfolio choice opportunity of the policyholders. However, it is common for policyholders to rebalance his portfolio in many types of VA products. Therefore it’s important for insurance companies to apply an approximate method to measure the guaranteed cost.
    In this research, we assume that there are two potential assets in policyholders’ portfolio; one with high risk and high return and the other one with low risk and low return. The utility function of the policyholder is assumed to follow a power utility. We consider the asset allocation effect on the guaranteed cost for a VA with guaranteed minimum withdrawal benefits, finding that the guaranteed cost will increase 12% compared with a specific underling asset.
    The model effect of the asset return process is also examined by considering two different asset processes, the lognormal model and ARIMA-GARCH model. The solution of dynamic programming problem is solved by the numerical approach proposed by Huang (2009). Finally we get the conclusion which the guaranteed cost given by the ARIMA-GARCH model is greater than the lognormal model.
    Reference: 1. Aase, K.K., and Persson, S.A., 1994, Pricing of Unit-linked Life Insurance Policies. Scandinavian Actuarial Journal 1, 26-52.
    2. Aase, K.K., and Persson, S.A., 1997, Valuation of the Minimum Guaranteed Return Embedded in Life Insurance Contracts. Journal of Risk and Insurance 64 (4), 599-617.
    3. Bacinello, A. R., Biffis, E., and Millossovich, P., 2009, Regression-Based Algorithm for Life Insurance Contracts with Surrender Guarantees, to appear in Quantitative Finance, Version as of April 7, 2009.
    4. Boyle, P.P., Schwartz, E., 1977. Equilibrium Prices of Guarantees under Equity-linked Contracts. Journal of Risk and Insurance 44(2), 639–680.
    5. Boyle, P.P. and Schwartz, E.S., 1997, Equilibrium Prices of Guarantees under Equity-linked Contracts. Journal of Risk and Insurance 44, 639-680.
    6. Boyle, P.P. and Hardy, M.R., 1997, Reserving for Maturity Guarantees: Two Approaches. Insurance: Mathematics and Economics 21, 113-127.
    7. Boyle, P.P. and Hardy, M.R. 2003, Guaranteed Annuity Options. Astin Bulletin 33 (2), 125-152
    8. Brennan, M.J., and Schwartz, E.S., 1976. The Pricing of Equity-linked Life Insurance Policies with an Asset Value Guarantee. Journal of Financial Economics 3 (1), 195–213.
    9. Brennan, M.J. and Schwartz, E.S., 1979, Alternative Investment Strategies for the Issuers of Equity-linked Life Insurance Policies with an Asset Value Guarantee, Journal of Business 52, 63-93.
    10. Coleman, T.F. ,Kim, Y., and Patron, M. (2005), Hedging Guaranteed Variable Annuities Under Both Equity and Interest Rate Risks, Cornell University, New York.
    11. Coleman, T.F. ,Kim, Y., and Patron, M. (2005), Robustly Hedging Variable Annuities With Guaranteed Under Jump and Volatility Risk, The Journal of Risk and Insurance, 2007, Vol. 74, No,2, 347-376.
    12. Chen, K. Verzal, and P. Forsyth. The effect of modeling parameters on the value of GMWB guarantees. Insurance: Mathematics and Economics, 43(1):165-173, 2008
    13. Delbaen, F., and M. Yor, 2002, Passport Options, Mathematical Finance, 12(4): 299-328.
    14. Hardy, M.R. 2000, Hedging and Reserving for Single-premium Segregated Fund Contracts. North American Actuarial Journal 4 (2), 63-74.
    15. Hardy, M.R., 2003, Investment Guarantees: Modeling and Risk Management for Equity-linked Life Insurance. 1st ed., Hoboken, N.J.: Wiley.
    16. Holz, D., Kling, A., and Ru, J. , 2007, GMWB For Life An Analysis of Lifetime Withdrawal Guarantees. Working Paper, Ulm University, 2007.
    17. Hung,D.Y.,2009,The numerical solution of optimal asset allocation dynamic programming. Cheng-Chi University master degree paper.
    18. Liu,Y,2006, 2010Pricing and Hedging the Guaranteed Minimum Withdrawal Benefits in Variable Annuities. Working Paper.
    19. Milevsky, M.A., and Posner, S.E., 2001, The Titanic option: Valuation of Guaranteed Minimum DEATH Benefit in Variable Annuities and Mutual Fund. The Journal of Risk and Insurance, Vol. 68, No. 1,91-216,2001.
    20. Milevsky, M.A., Salisbury, T.S., 2006. Financial Valuation of Guaranteed Minimum Withdrawal Benefits. Insurance: Mathematics and Economics 38, 21-38
    21. Nielsen, J.A., K. Sandmann, 1995, Equity-Linked Life Insurance: a Model with Stochastic Interest Rates. Insurances: Mathematics and Economics, 16,225-253.
    22. Turnbull. Understanding the true cost of VA hedging in volatile markets. Technical report, Nov 2008.
    23. J. Peng, K. Leung, and Y. Kwong. Pricing Guaranteed Minimal Withdrawal Benefit under the stochastic interest rate. Technical report, Jan 2009.
    Description: 碩士
    國立政治大學
    風險管理與保險研究所
    98358020
    99
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0098358020
    Data Type: thesis
    Appears in Collections:[風險管理與保險學系] 學位論文

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