學術產出-Theses

Article View/Open

Publication Export

Google ScholarTM

政大圖書館

Citation Infomation

  • No doi shows Citation Infomation
題名 同調風險測量值在保證給付投資型保險準備金提存之應用
作者 鄭宇宏
貢獻者 楊曉文<br>黃泓智
<br>
鄭宇宏
關鍵詞 同調風險測量值
變形函數
條件尾端期望值
尾端涉險值
保證年金選擇權
日期 2002
上傳時間 14-Sep-2009 09:42:11 (UTC+8)
摘要 Artzner等學者在1999年提出風險測量值應具備同調(coherent)性質,然而,涉險值並未能完全符合。本文針對Wirch & Hardy(1999)提出滿足Artzner et al.(1999)所定義同調性質之風險量化指標如條件尾端期望值(Conditional Tail Expectation;又稱尾端涉險值,Tail-VaR)以及危險比例(proportional hazards;PH)、雙重次方(dual power;DP)變形函數(distortion function)等風險衡量方法作探討,參考MGWP(1980)、Boyle & Hardy(1997)、Hardy(2000)、Yang(2001)、Wilkie & Waters & Yang(2003)對於附保證給付之投資連結型保險契約提存準備金的方法,將其應用到保險公司所發行的附保證給付之風險量化上,同時比較其與涉險值之差異。其中之數值分析將以附最低死亡保證給付(Guarantee Minimum Death Benefit)之變額年金,以及附保證年金選擇權(Guaranteed Annuity Options)之單位連結(Unit-linked)保險商品作為範例,分別以台灣、英國兩地的投資環境為背景,檢視其附保證給付之投資型保單可能面臨的風險暴露,提供保險公司作為提存投資型商品保證給付部分之責任準備金參考。
In this paper we introduce the properties of a coherent risk measure(Artzner et al(1999)). The risk measure of Value at Risk that does not adhere to the consistency requirements is discussed. We consider the coherent risk measures of conditional tail expectation(also known as Tail-VaR), proportional hazards and dual power distortion functions outlined by Wirch and Hardy(1999). MGWP(1980),Boyle and Hardy(1997),Hardy(2000),Yang(2001),Wilkie, Waters and Yang(2003)use VaR and the latter two papers also apply conditional tail expectation to reserve for investment-linked contracts with guaranteed risk. Instead, we apply the coherent measures to reserve two different types of guarantee:guarantee minimum death benefit and guaranteed annuity options attached to variable annuity contracts and unit-linked contracts separately. In addition, the comparison of the numerical results for VaR risk measure and coherent risk measure are analyzed.
參考文獻 一、中文部分
1.王棻瑩(2002),「附保證給付之投資型保險商品成本訂價:以變額年金保險死亡保證為例」,淡江大學保險經營研究所碩士論文
2.吳明政(1997),「變額年金精算及相關問題之探討」,逢甲大學保險學研究所碩士論文
3.李進生、謝文良、林允永、蔣炤坪、陳達新、盧陽正(2001),風險管理:風險值(VaR)理論與應用,清蔚科技出版
4.周大慶、沈大白、張大成、敬永康、柯瓊鳳(2002),風險管理新標竿:風險值理論與應用,智勝文化出版
5.林至岳(2002),「台灣投資型保險市場與發展」,保險發展事業中心研究報告
6.林姿婷(2001),「風險基礎資本與涉險值運用在保險監理上之比較」,政治大學風險管理與保險學研究所碩士論文
7.陳家明譯(2000),變額保險,財團法人保險事業發展中心發行
8.郭怡馨(1999),「保本型變額壽險之評價分析」,政治大學風險管理與保險學研究所碩士論文
9.張智星(2000),MATLAB程式設計與應用,清蔚科技出版
10.黃達業譯(2001),風險值:市場風險控管之新基準,台灣金融研訓院發行11.黃泓智、余清祥、楊曉文、黃彥富(2003),隨機投資模型之建立與長期負債之投資避險策略,投稿中論文
12.楊曉文&黃泓智(2003),「分紅保單和不分紅保單之研究」,執行中論文
13.楊曉文(2003),應用隨機模擬方法提存投資型保險之保證風險:以保證年金選擇權為例,投稿中論文
14.廖勇誠(1997),「變額年金保險與共同基金之比較分析」,逢甲大學保險學研究所碩士論文
二、英文部分
1.Artzner P., Delbaen F., Eber J.-M., Heath D.(1999),“Coherent Measures of Risk” Mathematical Finance 9(3):203-228
2.Artzner, P.(1999),“Application of Coherent Risk Measures to Capital Requirements in Insurance”, North American Actuarial Journal(2)2:11-25
3.Boyle, P. P. & Hardy M. R.(1997), “Reserving for Maturity Guarantees:Two Approaches”, Insurance: Mathematics and Economics, 21:113-127
4.CIA Task Force(2002), “Report of the CIA Task Force on Segregated Fund Investment Guarantees”
5.Darrel Duffie, Jun Pan(1997), “An Overview of Value at Risk”, Journal of Derivatives, 4:7-48
6.Goovaerts, DeVylder, F., and Haezendonce, J.(1984), Insurance Premiums, The Netherlands:North Holland
7.Hardy, M.R.(2000), “Hedging and Reserving for Single-Premium for Segregated Fund Contracts”, North American Actuarial Journal(4)2
8.Hardy, M.R.(1999), “Maturity Guarantees for Segregated Fund Contracts:Hedging and Reserving”, Presented at symposium, Risks in Investment Accumulation Products, New York
9.Hogg, R.V., Klugman, S.A.(1984), Loss Distributions, New York:Wiley
10.Jorion, P.(2000),Value at Risk-The New Benchmark for Managing Financial Risk, Chicago:McGraw-Hill Companies
11.Maturity Guarantees Working Party(MGWP)(1980), “Report of the Maturity Guarantees Working Party” Journal of the Institute of Actuaries, 107:103-209
12.Meyers, G..G..(2002), “Setting Capital Requirements with Coherent Measures of Risk”, Actuarial Review
13.Szego,G.,(2002)“Measures of risk”, Journal of Banking & Finance, 26:1253-1272
14.Wang, S.S., Young Virginia R.(1998)“Ordering risks:Expected utility theory versus Yarri’s dual theory of risk”, Insurance: Mathematics and Economics, 22:145-161
15.Wang, S.S.(1998), “An actuarial index of the right-tail risk”, Insurance: North American Actuarial Journal, 2(2):88-101
16.Wang, S.S., Young, V.R., Panjer, H.H.,(1997), “Axiomatic characterization of insurance prices”, Insurance: Mathematics and Economics, 21(2):173-183
17.Wang, S.S.(1996a), “Ordering of risks under PH-transforms”, Insurance: Mathematics and Economics, 18:109-114
18.Wang, S.S.(1996b), “Premium calculation by transforming the layer premium density”, ASTIN Bulletin 26:71-92
19.Wang, S.S.(1996c), “Risk measures with applications in insurance ratemaking actuarial valuation”, Technical report, University of Waterloo;Course Notes.
20.Wang, S.S.(1995), “Insurance pricing and increased limits ratemaking by proportional hazards transforms”, Insurance: Mathematics and Economics, 17:43-54
21.Wirch, J.L.(1999), Coherent Beta Risk Measures for Capital Requirements. Ph.D. Thesis, Waterloo University, Ontario
22.Wirch, J.L.(1999), “Raising Value At Risk”, North American Actuarial Journal(3)2:106-115
23.Wirch, J.L. & Hardy, M.R.(2000a), “Distortion Risk Measures:Coherence and Stochastic Dominance”, Working paper
24.Wirch, J.L. & Hardy, M.R.(2000b), “Proper Ordering for Risk Measures”, AFIR Congress Proceedings
25.Wirch, J.L. & Hardy, M.R.(1999), “A synthesis of risk measures for capital adequacy”, Insurance: Mathematics and Economics, 25:337-347
26.Wendy L. Martinez & Angel R. Martinez(2002), Computational Statistics Handbook with MATLAB, London:Chapman and Hall
27.Wilkie, A. D., Waters, H.R., Yang, S (2003), “Reserving, pricing and hedging for policies with guaranteed annuity option“, Forthcoming in British Actuarial Journal
28.Wilkie, A. D.(1995), “More on A Stochastic Asset Model for Actuarial Use”, British Actuarial Journal 1:777-964
29.Wilkie, A. D.(1986), “A Stochastic Investment Model for Actuarial Use”, Transactions of the Faculty of Actuaries, 39, pp.341-381.
30.Wilkie, A. D.(1976), “Universal or Variable Linked Life Assurances and Life Annuities”, Journal of the Institute of Actuaries:.221-228
31.Yang, S(2001), Reserving, pricing and hedging for guaranteed annuity option. Ph.D. Thesis, Heriot-Watt University, Edinburgh
32.Yarri, M.E.(1987), “The Dual Theory of Choice Under Risk”, Econometrica(55)1:95-115
33.Actuarial Guideline XXXIV / Minimum Guaranteed Benefits for Variable Annuities, 1998 Valuation Actuary Symposium Proceedings, Session 10PD, http://www.soa.org:80/library/valact/1985-99/VASP989.pdf
34.Minimum Guaranteed Benefits on Variable Annuities, 2000 Valuation Actuary Symposium, Session 17PD, http://www.soa.org:80/library/valact/2000-09/va00_17pd.pdf
35.Understanding And Managing The Risks Underlying Guaranteed Benefits In Variable Annuities, New Orleans Annual Meeting(SOA), http://www.soa.org:80/library/record/2000-09/rsa01v27n3160ts.pdf
36.Minimum Guaranteed Benefits on Variable Annuities, 2001 Valuation Actuary Symposium, Session 10PD, http://www.soa.org:80/library/valact/2000-09/va01_10pd.pdf
37.Guarantees on Variable Products:How Are Companies Assessing the Risks, Atlanta Spring Meeting(SOA), http://www.soa.org:80/library/record/1990-99/rsa99v25n190pd.pdf
38.Understanding and Managing Annuity Risks, Colorado Springs Spring Meeting(SOA), http://www.soa.org:80/library/record/2000-09/rsa02v28n111PD.pdf
39.Variable Annuities and Segregated Funds—Guaranteed Benefits Valuation Issues, San Francisco Annual Meeting(SOA), http://www.soa.org:80/library/record/1990-99/rsa99v25n3127pd.pdf
描述 碩士
國立政治大學
風險管理與保險研究所
90358017
91
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0903580171
資料類型 thesis
dc.contributor.advisor 楊曉文<br>黃泓智zh_TW
dc.contributor.advisor <br>en_US
dc.contributor.author (Authors) 鄭宇宏zh_TW
dc.creator (作者) 鄭宇宏zh_TW
dc.date (日期) 2002en_US
dc.date.accessioned 14-Sep-2009 09:42:11 (UTC+8)-
dc.date.available 14-Sep-2009 09:42:11 (UTC+8)-
dc.date.issued (上傳時間) 14-Sep-2009 09:42:11 (UTC+8)-
dc.identifier (Other Identifiers) G0903580171en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/31283-
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) 90358017zh_TW
dc.description (描述) 91zh_TW
dc.description.abstract (摘要) Artzner等學者在1999年提出風險測量值應具備同調(coherent)性質,然而,涉險值並未能完全符合。本文針對Wirch & Hardy(1999)提出滿足Artzner et al.(1999)所定義同調性質之風險量化指標如條件尾端期望值(Conditional Tail Expectation;又稱尾端涉險值,Tail-VaR)以及危險比例(proportional hazards;PH)、雙重次方(dual power;DP)變形函數(distortion function)等風險衡量方法作探討,參考MGWP(1980)、Boyle & Hardy(1997)、Hardy(2000)、Yang(2001)、Wilkie & Waters & Yang(2003)對於附保證給付之投資連結型保險契約提存準備金的方法,將其應用到保險公司所發行的附保證給付之風險量化上,同時比較其與涉險值之差異。其中之數值分析將以附最低死亡保證給付(Guarantee Minimum Death Benefit)之變額年金,以及附保證年金選擇權(Guaranteed Annuity Options)之單位連結(Unit-linked)保險商品作為範例,分別以台灣、英國兩地的投資環境為背景,檢視其附保證給付之投資型保單可能面臨的風險暴露,提供保險公司作為提存投資型商品保證給付部分之責任準備金參考。zh_TW
dc.description.abstract (摘要) In this paper we introduce the properties of a coherent risk measure(Artzner et al(1999)). The risk measure of Value at Risk that does not adhere to the consistency requirements is discussed. We consider the coherent risk measures of conditional tail expectation(also known as Tail-VaR), proportional hazards and dual power distortion functions outlined by Wirch and Hardy(1999). MGWP(1980),Boyle and Hardy(1997),Hardy(2000),Yang(2001),Wilkie, Waters and Yang(2003)use VaR and the latter two papers also apply conditional tail expectation to reserve for investment-linked contracts with guaranteed risk. Instead, we apply the coherent measures to reserve two different types of guarantee:guarantee minimum death benefit and guaranteed annuity options attached to variable annuity contracts and unit-linked contracts separately. In addition, the comparison of the numerical results for VaR risk measure and coherent risk measure are analyzed.en_US
dc.description.tableofcontents 第一章 緒論
     第一節 研究動機與目的……………………….............. 1
     第二節 研究範圍與限制…………………………..………... 3
     第三節 研究方法與步驟………………………………………. 4
     第四節 研究內容………………………………………………. 6
     第二章 風險衡量
     第一節 風險衡量之意義與發展……………………...………. 8
     第二節 保費原理之回顧………………………………………. 10
     第三章 現行風險衡量方法(VaR)之問題
     第一節 涉險值之回顧…………………………………………. 13
     第二節 涉險值與風險基礎資本額……………………………. 17
     第三節 涉險值的缺陷…………………………………………. 20
     第四節 改進現行風險衡量之方法……………………………. 25
     第四章 變形函數風險測量值之綜觀
     第一節 變形函數之特質………………………………………. 29
     第二節 特殊型態之變形函數…………………………………. 32
     第三節 範例……………………………………………………. 39
     第四節 變形函數之比較………………………………………. 41
     第五章 投資型商品之保證給付
     第一節 投資型保險商品………………………………………. 44
     第二節 投資型保險商品常見之保證給付……………………. 47
     第三節 保證給付相關文獻探討………………………………. 50
     第六章 應用同調風險測量值於準備金提存之實例說明
     第一節 投資模型之介紹………………………………………. 54
     第二節 死亡保證給付決定方式………………………………. 56
     第三節 變額年金附保證死亡給付之準備金提存……………. 59
     第四節 單位連結型契約附保證年金選擇權之準備金提存…. 71
     第五節 動態準備金之研究:以附GAO保單為例……………… 80
     第七章 結論與建議
     第一節 研究結論………………………………………………. 89
     第二節 後續研究與建議………………………………………. 91
     參考資料與文獻…………………………………………………. 93
     附錄一 貝他變形函數…………………………………………. 99
     附錄二 Wilkie Model結構與參數估計………………………. 102
     附錄三 Huang Model結構與參數估計………………………… 106
zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0903580171en_US
dc.subject (關鍵詞) 同調風險測量值zh_TW
dc.subject (關鍵詞) 變形函數zh_TW
dc.subject (關鍵詞) 條件尾端期望值zh_TW
dc.subject (關鍵詞) 尾端涉險值zh_TW
dc.subject (關鍵詞) 保證年金選擇權zh_TW
dc.title (題名) 同調風險測量值在保證給付投資型保險準備金提存之應用zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 一、中文部分zh_TW
dc.relation.reference (參考文獻) 1.王棻瑩(2002),「附保證給付之投資型保險商品成本訂價:以變額年金保險死亡保證為例」,淡江大學保險經營研究所碩士論文zh_TW
dc.relation.reference (參考文獻) 2.吳明政(1997),「變額年金精算及相關問題之探討」,逢甲大學保險學研究所碩士論文zh_TW
dc.relation.reference (參考文獻) 3.李進生、謝文良、林允永、蔣炤坪、陳達新、盧陽正(2001),風險管理:風險值(VaR)理論與應用,清蔚科技出版zh_TW
dc.relation.reference (參考文獻) 4.周大慶、沈大白、張大成、敬永康、柯瓊鳳(2002),風險管理新標竿:風險值理論與應用,智勝文化出版zh_TW
dc.relation.reference (參考文獻) 5.林至岳(2002),「台灣投資型保險市場與發展」,保險發展事業中心研究報告zh_TW
dc.relation.reference (參考文獻) 6.林姿婷(2001),「風險基礎資本與涉險值運用在保險監理上之比較」,政治大學風險管理與保險學研究所碩士論文zh_TW
dc.relation.reference (參考文獻) 7.陳家明譯(2000),變額保險,財團法人保險事業發展中心發行zh_TW
dc.relation.reference (參考文獻) 8.郭怡馨(1999),「保本型變額壽險之評價分析」,政治大學風險管理與保險學研究所碩士論文zh_TW
dc.relation.reference (參考文獻) 9.張智星(2000),MATLAB程式設計與應用,清蔚科技出版zh_TW
dc.relation.reference (參考文獻) 10.黃達業譯(2001),風險值:市場風險控管之新基準,台灣金融研訓院發行11.黃泓智、余清祥、楊曉文、黃彥富(2003),隨機投資模型之建立與長期負債之投資避險策略,投稿中論文zh_TW
dc.relation.reference (參考文獻) 12.楊曉文&黃泓智(2003),「分紅保單和不分紅保單之研究」,執行中論文zh_TW
dc.relation.reference (參考文獻) 13.楊曉文(2003),應用隨機模擬方法提存投資型保險之保證風險:以保證年金選擇權為例,投稿中論文zh_TW
dc.relation.reference (參考文獻) 14.廖勇誠(1997),「變額年金保險與共同基金之比較分析」,逢甲大學保險學研究所碩士論文zh_TW
dc.relation.reference (參考文獻) 二、英文部分zh_TW
dc.relation.reference (參考文獻) 1.Artzner P., Delbaen F., Eber J.-M., Heath D.(1999),“Coherent Measures of Risk” Mathematical Finance 9(3):203-228zh_TW
dc.relation.reference (參考文獻) 2.Artzner, P.(1999),“Application of Coherent Risk Measures to Capital Requirements in Insurance”, North American Actuarial Journal(2)2:11-25zh_TW
dc.relation.reference (參考文獻) 3.Boyle, P. P. & Hardy M. R.(1997), “Reserving for Maturity Guarantees:Two Approaches”, Insurance: Mathematics and Economics, 21:113-127zh_TW
dc.relation.reference (參考文獻) 4.CIA Task Force(2002), “Report of the CIA Task Force on Segregated Fund Investment Guarantees”zh_TW
dc.relation.reference (參考文獻) 5.Darrel Duffie, Jun Pan(1997), “An Overview of Value at Risk”, Journal of Derivatives, 4:7-48zh_TW
dc.relation.reference (參考文獻) 6.Goovaerts, DeVylder, F., and Haezendonce, J.(1984), Insurance Premiums, The Netherlands:North Hollandzh_TW
dc.relation.reference (參考文獻) 7.Hardy, M.R.(2000), “Hedging and Reserving for Single-Premium for Segregated Fund Contracts”, North American Actuarial Journal(4)2zh_TW
dc.relation.reference (參考文獻) 8.Hardy, M.R.(1999), “Maturity Guarantees for Segregated Fund Contracts:Hedging and Reserving”, Presented at symposium, Risks in Investment Accumulation Products, New Yorkzh_TW
dc.relation.reference (參考文獻) 9.Hogg, R.V., Klugman, S.A.(1984), Loss Distributions, New York:Wileyzh_TW
dc.relation.reference (參考文獻) 10.Jorion, P.(2000),Value at Risk-The New Benchmark for Managing Financial Risk, Chicago:McGraw-Hill Companieszh_TW
dc.relation.reference (參考文獻) 11.Maturity Guarantees Working Party(MGWP)(1980), “Report of the Maturity Guarantees Working Party” Journal of the Institute of Actuaries, 107:103-209zh_TW
dc.relation.reference (參考文獻) 12.Meyers, G..G..(2002), “Setting Capital Requirements with Coherent Measures of Risk”, Actuarial Reviewzh_TW
dc.relation.reference (參考文獻) 13.Szego,G.,(2002)“Measures of risk”, Journal of Banking & Finance, 26:1253-1272zh_TW
dc.relation.reference (參考文獻) 14.Wang, S.S., Young Virginia R.(1998)“Ordering risks:Expected utility theory versus Yarri’s dual theory of risk”, Insurance: Mathematics and Economics, 22:145-161zh_TW
dc.relation.reference (參考文獻) 15.Wang, S.S.(1998), “An actuarial index of the right-tail risk”, Insurance: North American Actuarial Journal, 2(2):88-101zh_TW
dc.relation.reference (參考文獻) 16.Wang, S.S., Young, V.R., Panjer, H.H.,(1997), “Axiomatic characterization of insurance prices”, Insurance: Mathematics and Economics, 21(2):173-183zh_TW
dc.relation.reference (參考文獻) 17.Wang, S.S.(1996a), “Ordering of risks under PH-transforms”, Insurance: Mathematics and Economics, 18:109-114zh_TW
dc.relation.reference (參考文獻) 18.Wang, S.S.(1996b), “Premium calculation by transforming the layer premium density”, ASTIN Bulletin 26:71-92zh_TW
dc.relation.reference (參考文獻) 19.Wang, S.S.(1996c), “Risk measures with applications in insurance ratemaking actuarial valuation”, Technical report, University of Waterloo;Course Notes.zh_TW
dc.relation.reference (參考文獻) 20.Wang, S.S.(1995), “Insurance pricing and increased limits ratemaking by proportional hazards transforms”, Insurance: Mathematics and Economics, 17:43-54zh_TW
dc.relation.reference (參考文獻) 21.Wirch, J.L.(1999), Coherent Beta Risk Measures for Capital Requirements. Ph.D. Thesis, Waterloo University, Ontariozh_TW
dc.relation.reference (參考文獻) 22.Wirch, J.L.(1999), “Raising Value At Risk”, North American Actuarial Journal(3)2:106-115zh_TW
dc.relation.reference (參考文獻) 23.Wirch, J.L. & Hardy, M.R.(2000a), “Distortion Risk Measures:Coherence and Stochastic Dominance”, Working paperzh_TW
dc.relation.reference (參考文獻) 24.Wirch, J.L. & Hardy, M.R.(2000b), “Proper Ordering for Risk Measures”, AFIR Congress Proceedingszh_TW
dc.relation.reference (參考文獻) 25.Wirch, J.L. & Hardy, M.R.(1999), “A synthesis of risk measures for capital adequacy”, Insurance: Mathematics and Economics, 25:337-347zh_TW
dc.relation.reference (參考文獻) 26.Wendy L. Martinez & Angel R. Martinez(2002), Computational Statistics Handbook with MATLAB, London:Chapman and Hallzh_TW
dc.relation.reference (參考文獻) 27.Wilkie, A. D., Waters, H.R., Yang, S (2003), “Reserving, pricing and hedging for policies with guaranteed annuity option“, Forthcoming in British Actuarial Journalzh_TW
dc.relation.reference (參考文獻) 28.Wilkie, A. D.(1995), “More on A Stochastic Asset Model for Actuarial Use”, British Actuarial Journal 1:777-964zh_TW
dc.relation.reference (參考文獻) 29.Wilkie, A. D.(1986), “A Stochastic Investment Model for Actuarial Use”, Transactions of the Faculty of Actuaries, 39, pp.341-381.zh_TW
dc.relation.reference (參考文獻) 30.Wilkie, A. D.(1976), “Universal or Variable Linked Life Assurances and Life Annuities”, Journal of the Institute of Actuaries:.221-228zh_TW
dc.relation.reference (參考文獻) 31.Yang, S(2001), Reserving, pricing and hedging for guaranteed annuity option. Ph.D. Thesis, Heriot-Watt University, Edinburghzh_TW
dc.relation.reference (參考文獻) 32.Yarri, M.E.(1987), “The Dual Theory of Choice Under Risk”, Econometrica(55)1:95-115zh_TW
dc.relation.reference (參考文獻) 33.Actuarial Guideline XXXIV / Minimum Guaranteed Benefits for Variable Annuities, 1998 Valuation Actuary Symposium Proceedings, Session 10PD, http://www.soa.org:80/library/valact/1985-99/VASP989.pdfzh_TW
dc.relation.reference (參考文獻) 34.Minimum Guaranteed Benefits on Variable Annuities, 2000 Valuation Actuary Symposium, Session 17PD, http://www.soa.org:80/library/valact/2000-09/va00_17pd.pdfzh_TW
dc.relation.reference (參考文獻) 35.Understanding And Managing The Risks Underlying Guaranteed Benefits In Variable Annuities, New Orleans Annual Meeting(SOA), http://www.soa.org:80/library/record/2000-09/rsa01v27n3160ts.pdfzh_TW
dc.relation.reference (參考文獻) 36.Minimum Guaranteed Benefits on Variable Annuities, 2001 Valuation Actuary Symposium, Session 10PD, http://www.soa.org:80/library/valact/2000-09/va01_10pd.pdfzh_TW
dc.relation.reference (參考文獻) 37.Guarantees on Variable Products:How Are Companies Assessing the Risks, Atlanta Spring Meeting(SOA), http://www.soa.org:80/library/record/1990-99/rsa99v25n190pd.pdfzh_TW
dc.relation.reference (參考文獻) 38.Understanding and Managing Annuity Risks, Colorado Springs Spring Meeting(SOA), http://www.soa.org:80/library/record/2000-09/rsa02v28n111PD.pdfzh_TW
dc.relation.reference (參考文獻) 39.Variable Annuities and Segregated Funds—Guaranteed Benefits Valuation Issues, San Francisco Annual Meeting(SOA), http://www.soa.org:80/library/record/1990-99/rsa99v25n3127pd.pdfzh_TW