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題名 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
作者 陳尚韋
貢獻者 黃泓智<br>李永崇
陳尚韋
關鍵詞 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
日期 2010
上傳時間 4-Sep-2013 15:01:56 (UTC+8)
摘要 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.
參考文獻 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.
描述 碩士
國立政治大學
風險管理與保險研究所
98358020
99
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0098358020
資料類型 thesis
dc.contributor.advisor 黃泓智<br>李永崇zh_TW
dc.contributor.author (Authors) 陳尚韋zh_TW
dc.creator (作者) 陳尚韋zh_TW
dc.date (日期) 2010en_US
dc.date.accessioned 4-Sep-2013 15:01:56 (UTC+8)-
dc.date.available 4-Sep-2013 15:01:56 (UTC+8)-
dc.date.issued (上傳時間) 4-Sep-2013 15:01:56 (UTC+8)-
dc.identifier (Other Identifiers) G0098358020en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60051-
dc.description (描述) 碩士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) 98358020zh_TW
dc.description (描述) 99zh_TW
dc.description.abstract (摘要) 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。		zh_TW
dc.description.abstract (摘要) 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.		en_US
dc.description.tableofcontents CATALOG I
LIST OF TABLE II
LIST OF FIGURE III
1 INTRODUCTION 1
2 LITERATURE REVIEW 4
2.1 PRICING OF GMWB 4
2.2 BASIC TYPE OF GUARANTEED PRODUCT 6
3 METHODOLOGY 8
3.1 DESIGN OF GUARANTEED MINIMUM BENEFIT 8
3.2 ASSET MODEL 10
3.3 UTILITY FUNCTION 12
3.4 PARAMETER ESTIMATION 12
4 NUMERICAL RESULTS 18
4.1 RESULT OF SIMULATION 18
4.2 ANALYST OF RESULT 21
4.3 THE IMPROVEMENT OF THE POLICYHOLDER’S EXPECTED UTILITY 28
4.4 THE RESULT OF VA WITH GMMB 29
5 SENSITIVITY ANALYSIS 31
5.1 SENSITIVITY ANALYSIS OF THE RISK-AVERSE PARAMETER 31
5.2 SENSITIVITY ANALYSIS OF MODEL 35
6 CONCLUSION 37
REFERENCE 39
APPENDIX A. THE DATA OF THE MAIN FIVE INDEXES IN U.S. 41
APPENDIX B. THE DECISION TABLE OF GMMB 43		zh_TW
dc.format.extent 1121606 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0098358020en_US
dc.subject (關鍵詞) 附投資保證提領保險商品zh_TW
dc.subject (關鍵詞) 變額年金zh_TW
dc.subject (關鍵詞) 動態規劃求解zh_TW
dc.subject (關鍵詞) 冪次效用函數zh_TW
dc.subject (關鍵詞) ARIMA-GARCH 模型zh_TW
dc.subject (關鍵詞) GMWBen_US
dc.subject (關鍵詞) Variable Annuitiesen_US
dc.subject (關鍵詞) Dynamic Programmingen_US
dc.subject (關鍵詞) Power Utility Functionen_US
dc.subject (關鍵詞) ARIMA-GARCH modelen_US
dc.title (題名) 附最低保證變額年金保險最適資產配置及準備金之研究zh_TW
dc.title (題名) A study of optimal asset allocation and reserve for variable annuities insurance with guaranteed minimum benefiten_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 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.		zh_TW