結論與建議

保險密度與保險滲透度為兩個常常被用來衡量保險產業的指標，保險密度定 義為一個國家的保費收入除以總人口數，也就是每人平均保費支出。保險滲透度 則定義為一個國家的保費收入除以 GDP，也就是保費收入對 GDP 的比率，將台灣 與鄰近的日本做一比較，2006 年日本的保險密度為全球第 9，平均每人壽險保費 支出為 2829 美元，台灣的保險密度為全球第 20，平均每人壽險保費支出為 1800 美元。2007 年日本的保險密度為全球第 14，平均每人壽險保費支出為 2583 美元，

台灣則為第 19，平均每人壽險保費支出為 2165 美元[17]。顯示出台灣的壽險業 不斷的在成長，而且未來還有很大的成長空間。而近年來各壽險公司也在推廣業 務上做許多的努力，可以預見，未來台灣的壽險業保險密度逐漸上升，已經是必 然的趨勢。而隨著保險密度逐漸增加，保戶在面臨某些情況而不再需要既有之人 壽保單，而希望能夠將之做某些處理以達到減輕財務上的負擔時，如果只能依靠 解約、減額繳清或者展期等方法，對於保戶來說是無法符合其需求的。相反的，

如果有一個保險的次級市場可以做買賣，不僅可較滿足此類保戶的需求，對於整 個保險市場，也可期待因為保險商品流動性的提升，進而吸引更多的客戶願意購 買保險產品，做符合其需求的保險規劃，達到分散人身風險的效果，並使保險業 更蓬勃發展。

保單貼現證券即為保險的次級市場的投資工具，由於此商品本身的性質具有 爭議性的關係，需要嚴謹且完整的法律規範才有可能開放於市場交易，因此台灣 目前並沒有開放此商品給投資人投資。不過如同前段所述，這項商品的開放不僅 僅是讓投資人多一個投資工具的選擇，更能促進保險業的發展，因此可以預期未 來將會漸漸的參考國內外學者的研究，訂出完整的相關法規，並開放此商品於市 場上供投資人投資。

本文將保單貼現證券對於各項評價因素做了敏感度分析，以期能幫助投資人 稍微了解各項評價因素如何影響保單貼現證券之各個參與者收支。本文也將保單

52

貼現證券與幾個較為台灣投資人熟悉的投資工具做競爭力的分析，以期能夠幫助 投資人稍微了解保單貼現證券之報酬與風險的狀況，並且得到了保單貼現證券與 其他投資工具相比，依然有其競爭力的結果。最後本文也分析了各個不同情境的 生命預期對保單貼現證券報酬率的影響，以期能幫助投資人了解保單貼現證券最 大的不確定因素，即生命預期的變動是如何的影響此商品的報酬。本文所使用的 生命表為台灣壽險業第四回經驗生命表，而隨著時間過去，本文所使用之方法需 要配合最新的生命表才可得到更貼近事實的結論。並且由於台灣目前並未開放保 單貼現交易，因此本文所使用之保單貼現群組證券是參考美國的保單貼現範例，

未來若台灣開始開放保單貼現交易，可運用本文之方法於台灣的保單貼現實際案 例，以期能得到更適合台灣投資人參考之結論。

53

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British Actuarial Journal

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[2] Nancy L. Breuer, Financial Help for Terminally I11,

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[3] Alex Cowley and J. David Cummins, Securitization of Life Insurance Assets and Liabilities,

Journal of Risk and Insurance

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[4] Neil A. Doherty and Hal J. Singer, The Benefit of a Secondary Market for Life Insurance Policies,

Real Property, Probate and Trust Journal

, Vol.38,No.3,pp.449-478, 2003.

[5] Dam, J. L., Sale of life insurance is new option in estate planning, bankruptcy, divorce,

Lawyers Weekly USA,

網址：

http://www.logos4me.com/Articles/Lawyers%20Weekly%20USA.htm, 2000

[6] Emmanuel Modu, Life Settlement Securitization,

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Methodology,

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[7] Charles A. Stone and Anne Zissu, Securitization of Senior Life Settlements: Managing Extension Risk,

The Journal of Derivatives

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[8] Charles A. Stone and Anne Zissu, Using Life Extension-Duration and Life Extension-Convexity to Value Senior Life Settlement Contracts,

The Journal of Alternative Investments

, Vol.11, No.2, pp.94-110, 2008.

[9] CMG Surety LLC, Trustee, Secure Growth America Trust Series III Private Placement Memorandum, 2004.

[10] 陳文達,李阿乙,廖咸興，資產證券化理論與實務，智勝文化，2002.

54

[11] 林裕峰，保單貼現之設計與投資風險之分析，輔仁大學金融學研究所未出 版碩士論文，2003.

[12] 陳文國，我國推行壽險保單貼現可行性分析，逢甲大學保險學研究所未出 版碩士論文，2000.

[13] 林郁雯，保單暨壽險貼現法制之研究－以美國德州保單暨壽險貼現辦法為 例，高雄第一科技大學金融營運系未出版碩士論文，2006.

[14] 呂紹義，利用隨機死亡率模式建構現金流量參數模型與二元界限選擇權模 型探討壽險保單貼現證券之定價，高雄第一科技大學風險管理與保險系未出版碩 士論文，2006.

[15] 鄭百亨，保單貼現證券化之研究，台灣大學財務金融學研究所未出版碩士 論文，2005.

[16] 陳右越，保單貼現市場與評價之敏感度分析，台灣大學財務金融研究所未 出版碩士論文，2005.

[17] 現代保險健康理財雜誌，網址：http://www.rmim.com.tw/images/237-2007 全球保險市場總回顧.pdf，2007.

55

附錄一 保單貼現群組證券 各期預期現金流量及投資人 IRR 計算(LE= +0 )

Y e a r

Total Net Cash Flow

Policy 1

Policy 2

Policy 3

Policy 4

Policy 5

Policy 6

Policy 7

Policy 8

Policy 9

Policy 10

Policy 11

Policy 12

Policy 13

Policy 14

Policy 15

IRR 18.15% 16.75% 30.24% 26.52% 20.91% 23.71% 14.84% 20.90% 23.88% 20.33% 23.70% 13.62% 13.06% 18.38% 12.21% 25.47%

0 -12250000 -594000 -258000 -334000 -305000 -1283000 -2095000 -1710000 -424000 -53000 -500000 -483000 -2390000 -391000 -1100000 -330000 1 3732712 125286 86892 136073 99235 367984 594015 553078 235550 29444 167687 286686 618610 124693 195248 112231 2 3282181 123904 79381 116820 91727 360311 533916 493608 151813 18977 152881 165252 577421 114320 195554 106296 3 2888050 120656 70476 96357 82825 348460 465912 426560 133665 10708 134909 74817 528438 102291 193257 98719 4 2681227 115473 109627 107467 72699 332366 392300 491164 84236 10530 114215 11476 472926 88947 188151 89650

5 2496383 138336 98497 86995 61585 312156 426840 416090 49547 6193 91422 49905 412666 74743 180076 91332

6 2218294 129294 86689 67782 49779 331104 350543 341330 26890 3361 147332 24944 349939 60224 168995 80088

7 1838038 118502 74564 50563 37638 303671 277548 269939 13271 1659 122872 11216 287264 45995 155011 68325

8 1497875 106228 62508 35885 25559 273496 210761 204778 5845 731 99050 4441 227209 46456 138424 56504

9 1253222 92879 50916 24048 50941 241402 152577 148125 2240 280 76828 1505 172177 34498 159692 45114

10 969436 78949 40157 15079 40154 208362 104542 101440 721 90 57034 418 124139 24322 139419 34610

11 727476 64980 30544 8749 30512 175436 67204 65204 184 23 40267 89 84418 16144 118352 25370

12 528792 51547 22303 4633 22243 143687 40097 38929 34 4 26837 13 53503 9987 97323 17652

13 371971 39197 15548 2199 15470 114112 21907 21305 4 0 16732 1 31041 5685 77205 11565

14 253031 28391 10284 914 10197 87556 10771 10512 0 0 9652 0 15964 2930 58792 7068

15 166226 19436 6404 322 6319 64639 4659 4575 0 0 5082 0 6741 1337 42731 3981

16 105123 12457 3721 91 3647 45697 1717 1704 0 0 2400 0 1688 525 29439 2037

17 65689 7386 1995 19 1936 30770 514 520 0 0 994 0 1390 169 19067 929

18 38406 3990 973 3 932 19608 116 121 0 0 349 0 409 42 11495 368

19 21211 1925 424 0 398 11737 17 19 0 0 100 0 90 7 6372 122

20 10920 807 161 0 147 6540 1 1 0 0 21 0 12 0 3198 32

21 5169 283 52 0 45 3356 0 0 0 0 3 0 0 0 1424 6

22 2216 78 13 0 11 1565 0 0 0 0 0 0 0 0 548 1

23 847 15 3 0 2 652 0 0 0 0 0 0 0 0 175 0

24 284 2 0 0 0 238 0 0 0 0 0 0 0 0 44 0

25 74 0 0 0 0 74 0 0 0 0 0 0 0 0 8 0

26 19 0 0 0 0 19 0 0 0 0 0 0 0 0 0 0

27 4 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0

28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

56

保單貼現群組證券 各期預期現金流量及投資人 IRR 計算(LE= -12 )

Y e a r

Total Net Cash Flow

Policy 1

Policy 2

Policy 3

Policy 4

Policy 5

Policy 6

Policy 7

Policy 8

Policy 9

Policy 10

Policy 11

Policy 12

Policy 13

Policy 14

Policy 15

IRR 24.25% 20.74% 37.79% 38.16% 29.49% 29.16% 20.26% 28.61% 43.64% 43.54% 33.51% 36.44% 16.95% 25.13% 15.05% 33.15%

0 -12250000 -594000 -258000 -334000 -305000 -1283000 -2095000 -1710000 -424000 -53000 -500000 -483000 -2390000 -391000 -1100000 -330000 1 5707596 171034 132120 213078 144093 478885 884179 834795 462931 57799 258147 617570 856174 179948 260921 155922 2 4210162 162466 113140 160500 125226 453316 721538 675463 153688 19211 217665 122074 742887 151517 252576 138895 3 3289728 151231 93110 112795 105300 422275 561868 519315 66807 8351 174995 -35700 625886 122869 240334 120292 4 2714701 137529 72631 103616 84920 386281 411873 509803 17497 2187 131818 -73545 509861 95168 224255 100807

5 2362082 151679 101656 69985 64739 346159 388428 378576 3267 408 89892 374 399615 69541 204547 93216

6 1926634 134126 82284 44194 45411 345957 273913 266905 344 43 130920 0 299618 46954 181647 74318

7 1444059 115463 64418 25782 27555 300932 181815 177163 6 1 96364 0 213370 28094 156219 56877

8 1055940 96398 48567 13687 11692 255486 112416 109598 0 0 67286 0 143018 27086 129173 41533

9 811748 77729 35085 6482 35185 211102 63914 62390 0 0 44201 0 89151 16217 141558 28734

10 565343 60228 24142 2666 24211 169224 32860 32152 0 0 27039 0 50800 8860 114489 18672

11 383311 44569 15713 916 15749 131131 14941 14677 0 0 15209 0 25724 4331 89074 11277

12 253119 31267 9592 247 9601 97811 5825 5760 0 0 7738 0 10896 1845 66290 6247

13 162402 20607 5436 47 5427 69888 1860 1860 0 0 3486 0 3129 659 46883 3120

14 100529 12621 2823 5 2806 47563 451 460 0 0 1350 0 -371 186 31262 1373

15 59260 7082 1321 0 1304 30627 72 76 0 0 431 0 -1671 37 19464 517

16 32581 3574 545 0 533 18512 5 6 0 0 106 0 -2043 4 11181 158

17 18261 1582 193 0 185 10403 0 0 0 0 18 0 7 0 5836 37

18 8793 593 56 0 52 5372 0 0 0 0 1 0 0 0 2713 6

19 3807 178 12 0 11 2512 0 0 0 0 0 0 0 0 1094 0

20 1454 39 2 0 1 1044 0 0 0 0 0 0 0 0 368 0

21 478 5 0 0 0 376 0 0 0 0 0 0 0 0 97 0

22 131 0 0 0 0 113 0 0 0 0 0 0 0 0 18 0

23 29 0 0 0 0 27 0 0 0 0 0 0 0 0 2 0

24 5 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0

25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

57

保單貼現群組證券 各期預期現金流量及投資人 IRR 計算(LE= +12 )

Y e a r

Total Net Cash Flow

Policy 1

Policy 2

Policy 3

Policy 4

Policy 5

Policy 6

Policy 7

Policy 8

Policy 9

Policy 10

Policy 11

Policy 12

Policy 13

Policy 14

Policy 15

IRR 14.47% 13.98% 23.88% 20.03% 15.76% 23.71% 11.66% 14.02% 16.12% 13.35% 17.98% 7.91% 10.58% 14.36% 10.25% 20.51%

0 -12250000 -594000 -258000 -334000 -305000 -1283000 -2095000 -1710000 -424000 -53000 -500000 -483000 -2390000 -391000 -1100000 -330000

1 2696035 93391 57071 91276 69330 367984 418958 379912 139143 17392 109534 159081 469175 90804 149179 83805

2 2543519 95193 54674 84325 66948 360311 398779 360078 108494 13561 105508 114860 457360 87579 153278 82571

3 2408270 95805 51188 75795 63480 348460 371579 333464 127148 9894 99083 73988 439487 82998 155744 80157

4 2382430 95091 95891 97880 58921 332366 337757 398686 100031 12504 90247 37579 415538 77080 156329 76530

5 2374749 122926 90245 86869 53309 312156 409066 355310 75905 9488 79086 86218 385804 69919 154778 83670

6 2239127 119208 83633 75147 46722 331104 364591 308750 55302 6913 145816 60661 350976 61688 150885 77731

7 1968551 113884 76195 63164 39293 303671 316825 260785 38483 4810 130789 40672 312063 52649 144514 70754

8 1706945 106975 68115 51398 31214 273496 267551 213337 25421 3178 114501 25829 270369 56941 135653 62967

9 1511345 98605 59622 40320 59715 241402 218772 168324 15825 1978 97553 15427 227463 47309 164389 54641

10 1249277 88982 50978 30346 51057 208362 172473 127471 9204 1151 80611 8596 185066 37958 150932 46090

11 1005004 78391 42464 21787 42519 175436 130450 92133 4949 619 64353 4425 144928 29267 135628 37655

12 784724 67201 34357 14824 34381 143687 94108 63132 2429 304 49411 2080 108611 21563 118962 29674

13 593038 55847 26908 9485 26897 114112 64309 40691 1070 134 36299 879 77327 15079 101551 22450

14 432514 44806 20319 5655 20276 87556 41286 24439 414 52 25362 328 51798 9928 84079 16216

15 303486 34531 14727 3106 14659 64639 24655 13522 137 17 16735 106 32195 6093 67254 11110

16 204179 25411 10191 1549 10108 45697 13529 6793 37 5 10343 28 18143 3443 51736 7166

17 133294 17727 6692 689 6604 30770 6719 3042 8 1 5927 6 10959 1764 38073 4313

18 82125 11622 4141 268 4057 19608 2960 1185 1 0 3110 1 5337 803 26637 2395

19 48020 7085 2394 88 2322 11737 1126 389 0 0 1472 0 2290 316 17590 1211

20 26463 3963 1279 23 1224 6540 356 102 0 0 617 0 840 103 10868 548

21 13615 1999 624 5 586 3356 89 20 0 0 223 0 252 26 6218 217

22 6451 889 273 0 250 1565 16 3 0 0 67 0 58 5 3252 73

23 2763 337 105 0 93 652 2 0 0 0 16 0 9 0 1529 20

24 1047 104 35 0 29 238 0 0 0 0 3 0 1 0 633 4

25 340 24 9 0 7 74 0 0 0 0 0 0 0 0 225 1

26 92 4 2 0 1 19 0 0 0 0 0 0 0 0 66 0

27 19 0 0 0 0 4 0 0 0 0 0 0 0 0 15 0

28 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0

58

保單貼現群組證券 各期預期現金流量及投資人 IRR 計算(LE= +24 )

Y e a r

Total Net Cash Flow

Policy 1

Policy 2

Policy 3

Policy 4

Policy 5

Policy 6

Policy 7

Policy 8

Policy 9

Policy 10

Policy 11

Policy 12

Policy 13

Policy 14

Policy 15

IRR 11.88% 11.97% 19.60% 16.05% 12.47% 16.94% 9.52% 13.27% 12.10% 9.87% 14.35% 5.48% 8.86% 11.70% 8.78% 17.12%

0 -12250000 -594000 -258000 -334000 -305000 -1283000 -2095000 -1710000 -424000 -53000 -500000 -483000 -2390000 -391000 -1100000 -330000

1 1884201 70195 36197 63085 48230 228815 300015 264641 87375 10922 69689 90826 367635 67965 114283 64328

2 1861666 73371 36222 61204 48288 234083 297537 262012 74767 9346 70461 72586 368739 67873 120007 65170

3 1862125 75830 35490 58134 47596 237471 290199 254667 109207 7651 69636 53557 365809 66863 124777 65238

4 2012933 77440 83225 85858 46094 238699 277757 379357 95095 11887 67066 34319 358456 64857 128374 64449

5 2146120 108063 80809 80413 43742 237537 371140 361984 80872 10109 62645 95286 346422 61811 130550 74737

6 2144062 107553 77525 73910 40519 276780 348447 339679 66992 8374 136330 77425 329682 57722 131064 72060

7 1995349 105786 73394 66522 36440 270275 321079 312830 53896 6737 128160 61057 308407 52652 129701 68413

8 1839728 102669 68470 58486 31561 260935 289710 282148 41973 5247 118290 46583 282985 60526 126310 63835

9 1730686 98176 62845 50089 62976 248775 255344 248602 31521 3940 106968 34265 254077 53888 160793 58427

10 1533136 92337 56651 41655 56812 233930 219209 213389 22732 2841 94545 24208 222596 46771 153121 52339

11 1329991 85235 50059 33517 50234 216656 182706 177865 15665 1958 81455 16359 189706 39442 143362 45772

12 1127622 77033 43268 25989 43440 197328 147293 143444 10258 1282 68199 10524 156702 32201 131696 38965

13 932437 67976 36492 19331 36646 176437 114366 111463 6340 793 55297 6410 124920 25340 118441 32185

14 750382 58392 29950 13720 30074 154577 85100 83058 3671 459 43251 3674 95606 19127 104024 25699

15 586422 48657 23846 9236 23933 132416 60342 59031 1973 247 32490 1968 69797 13766 88967 19753

16 444066 39166 18354 5855 18401 110652 40502 39764 973 122 23324 979 48195 9381 73852 14546

17 327250 30306 13603 3465 13612 89969 25534 25200 435 54 15907 448 33226 6003 59282 10206

18 231778 22413 9664 1897 9641 70973 14979 14890 173 22 10236 187 20530 3571 45821 6781

19 158254 15736 6548 950 6502 54147 8082 8117 60 8 6166 70 11746 1951 33938 4233

20 103988 10404 4205 429 4148 39805 3955 4033 18 2 3446 23 6143 964 23952 2461

21 65633 6413 2542 172 2484 28083 1725 1798 4 1 1768 7 2889 422 16005 1320

22 39684 3640 1434 60 1384 18929 656 706 1 0 823 2 1196 159 10049 645

23 22898 1873 748 18 709 12129 211 238 0 0 342 0 424 50 5873 283

24 12542 855 356 4 329 7346 55 67 0 0 124 0 124 12 3161 109

25 6480 337 153 1 136 4177 11 15 0 0 38 0 28 2 1546 36

26 3134 110 58 0 49 2213 1 2 0 0 10 0 4 0 677 10

27 1409 28 19 0 15 1083 0 0 0 0 2 0 0 0 260 2

28 584 5 5 0 4 485 0 0 0 0 0 0 0 0 85 0

29 221 0 1 0 1 196 0 0 0 0 0 0 0 0 23 0

30 76 0 0 0 0 71 0 0 0 0 0 0 0 0 5 0

59

附錄二 臺灣壽險業第四回經驗生命表(男)

年齡

x

生存數

lx

死亡數

dx

死亡率

qx

平均餘命

ex

生存人年數

Lx T_x

0 10,000,000 57,300 0.005730 72.91 9,971,350 729,073,772

1 9,942,700 9,625 0.000968 72.32 9,937,888 719,102,422

2 9,933,075 7,470 0.000752 71.39 9,929,340 709,164,534

3 9,925,605 5,797 0.000584 70.45 9,922,707 699,235,194

4 9,919,808 4,682 0.000472 69.49 9,917,467 689,312,487

5 9,915,126 3,887 0.000392 68.52 9,913,183 679,395,020

6 9,911,239 3,489 0.000352 67.55 9,909,495 669,481,837

7 9,907,750 3,250 0.000328 66.57 9,906,125 659,572,342

8 9,904,500 3,169 0.000320 65.59 9,902,916 649,666,217

9 9,901,331 3,089 0.000312 64.61 9,899,787 639,763,301

10 9,898,242 2,930 0.000296 63.63 9,896,777 629,863,514

11 9,895,312 2,850 0.000288 62.65 9,893,887 619,966,737

12 9,892,462 3,007 0.000304 61.67 9,890,959 610,072,850

13 9,889,455 3,718 0.000376 60.69 9,887,596 600,181,891

14 9,885,737 5,220 0.000528 59.71 9,883,127 590,294,295

15 9,880,517 7,430 0.000752 58.74 9,876,802 580,411,168

16 9,873,087 10,031 0.001016 57.79 9,868,072 570,534,366

17 9,863,056 12,427 0.001260 56.85 9,856,843 560,666,294

18 9,850,629 12,688 0.001288 55.92 9,844,285 550,809,451

19 9,837,941 12,839 0.001305 54.99 9,831,522 540,965,166

20 9,825,102 12,900 0.001313 54.06 9,818,652 531,133,644

21 9,812,202 12,903 0.001315 53.13 9,805,751 521,314,992

22 9,799,299 12,857 0.001312 52.20 9,792,871 511,509,241

23 9,786,442 12,791 0.001307 51.27 9,780,047 501,716,370

24 9,773,651 12,716 0.001301 50.33 9,767,293 491,936,323

25 9,760,935 12,670 0.001298 49.40 9,754,600 482,169,030

26 9,748,265 12,663 0.001299 48.46 9,741,934 472,414,430

27 9,735,602 12,724 0.001307 47.52 9,729,240 462,672,496

28 9,722,878 12,863 0.001323 46.59 9,716,447 452,943,256

29 9,710,015 13,118 0.001351 45.65 9,703,456 443,226,809

30 9,696,897 13,508 0.001393 44.71 9,690,143 433,523,353

31 9,683,389 14,060 0.001452 43.77 9,676,359 423,833,210

32 9,669,329 14,794 0.001530 42.83 9,661,932 414,156,851

33 9,654,535 15,737 0.001630 41.90 9,646,667 404,494,919

34 9,638,798 16,868 0.001750 40.96 9,630,364 394,848,252

35 9,621,930 18,147 0.001886 40.04 9,612,857 385,217,888

36 9,603,783 19,563 0.002037 39.11 9,594,002 375,605,031

37 9,584,220 21,095 0.002201 38.19 9,573,673 366,011,029

38 9,563,125 22,703 0.002374 37.27 9,551,774 356,437,356

39 9,540,422 24,423 0.002560 36.36 9,528,211 346,885,582

40 9,515,999 26,274 0.002761 35.45 9,502,862 337,357,371

41 9,489,725 28,279 0.002980 34.55 9,475,586 327,854,509

42 9,461,446 30,466 0.003220 33.65 9,446,213 318,378,923

43 9,430,980 32,858 0.003484 32.76 9,414,551 308,932,710

44 9,398,122 35,440 0.003771 31.87 9,380,402 299,518,159

45 9,362,682 38,237 0.004084 30.99 9,343,564 290,137,757

46 9,324,445 41,223 0.004421 30.11 9,303,834 280,794,193

47 9,283,222 44,411 0.004784 29.25 9,261,017 271,490,359

48 9,238,811 47,811 0.005175 28.38 9,214,906 262,229,342

49 9,191,000 51,442 0.005597 27.53 9,165,279 253,014,436

50 9,139,558 55,349 0.006056 26.68 9,111,884 243,849,157

51 9,084,209 59,574 0.006558 25.84 9,054,422 234,737,273

52 9,024,635 64,147 0.007108 25.01 8,992,562 225,682,851

53 8,960,488 69,112 0.007713 24.18 8,925,932 216,690,289

54 8,891,376 74,510 0.008380 23.37 8,854,121 207,764,357

55 8,816,866 80,392 0.009118 22.56 8,776,670 198,910,236

56 8,736,474 86,797 0.009935 21x ...

76 8,693,076 190,133,566

60

57 8,649,677 93,754 0.010839 20.98 8,602,800 181,440,490

58 8,555,923 101,302 0.011840 20.20 8,505,272 172,837,690

59 8,454,621 109,437 0.012944 19.44 8,399,903 164,332,418

60 8,345,184 118,151 0.014158 18.69 8,286,109 155,932,515

61 8,227,033 127,420 0.015488 17.95 8,163,323 147,646,406

62 8,099,613 137,224 0.016942 17.22 8,031,001 139,483,083

63 7,962,389 147,527 0.018528 16.51 7,888,626 131,452,082

64 7,814,862 158,337 0.020261 15.81 7,735,694 123,563,456

65 7,656,525 169,646 0.022157 15.13 7,571,702 115,827,762

66 7,486,879 181,430 0.024233 14.46 7,396,164 108,256,060

67 7,305,449 193,631 0.026505 13.81 7,208,634 100,859,896

68 7,111,818 206,186 0.028992 13.17 7,008,725 93,651,262

69 6,905,632 219,012 0.031715 12.55 6,796,126 86,642,537

70 6,686,620 232,012 0.034698 11.94 6,570,614 79,846,411

71 6,454,608 245,036 0.037963 11.35 6,332,090 73,275,797

72 6,209,572 257,915 0.041535 10.78 6,080,615 66,943,707

73 5,951,657 270,419 0.045436 10.23 5,816,448 60,863,092

74 5,681,238 282,363 0.049701 9.69 5,540,057 55,046,644

75 5,398,875 293,499 0.054363 9.17 5,252,126 49,506,587

76 5,105,376 303,550 0.059457 8.67 4,953,601 44,254,461

77 4,801,826 312,196 0.065016 8.18 4,645,728 39,300,860

78 4,489,630 319,109 0.071077 7.72 4,330,076 34,655,132

79 4,170,521 323,991 0.077686 7.27 4,008,526 30,325,056

80 3,846,530 326,528 0.084889 6.84 3,683,266 26,316,530

81 3,520,002 326,424 0.092734 6.43 3,356,790 22,633,264

82 3,193,578 323,407 0.101268 6.04 3,031,875 19,276,474

83 2,870,171 317,274 0.110542 5.66 2,711,534 16,244,599

84 2,552,897 307,907 0.120611 5.30 2,398,944 13,533,065

85 2,244,990 295,297 0.131536 4.96 2,097,342 11,134,121

86 1,949,693 279,537 0.143375 4.63 1,809,925 9,036,779

87 1,670,156 260,858 0.156188 4.33 1,539,727 7,226,854

88 1,409,298 239,627 0.170033 4.04 1,289,485 5,687,127

89 1,169,671 216,354 0.184970 3.76 1,061,494 4,397,642

90 953,317 191,669 0.201055 3.50 857,483 3,336,148

91 761,648 166,304 0.218348 3.25 678,496 2,478,665

92 595,344 141,041 0.236907 3.02 524,824 1,800,169

93 454,303 116,657 0.256783 2.81 395,975 1,275,345

94 337,646 93,867 0.278003 2.60 290,713 879,370

95 243,779 73,277 0.300589 2.41 207,141 588,657

96 170,502 55,338 0.324559 2.24 142,833 381,516

97 115,164 40,300 0.349936 2.07 95,014 238,683

98 74,864 28,203 0.376717 1.92 60,763 143,669

99 46,661 18,889 0.404815 1.78 37,217 82,906

100 27,772 12,056 0.434119 1.65 21,744 45,689

101 15,716 7,300 0.464520 1.52 12,066 23,945

102 8,416 4,174 0.495908 1.41 6,329 11,879

103 4,242 2,241 0.528175 1.31 3,122 5,550

104 2,001 1,123 0.561225 1.21 1,440 2,428

105 878 522 0.594967 1.12 617 988

106 356 224 0.629307 1.04 244 371

107 132 88 0.664152 0.96 88 127

108 44 31 0.698078 0.88 29 39

109 13 10 0.731384 0.73 8 10

110 3 3 1.000000 0.50 2 2

61

臺灣壽險業第四回經驗生命表(女)

年齡

x

生存數

lx

死亡數

dx

死亡率

qx

平均餘命

ex

生存人年數

Lx T_x

0 10,000,000 52,400 0.005240 79.61 9,973,800 796,113,496

1 9,947,600 8,993 0.000904 79.03 9,943,104 786,139,696

2 9,938,607 6,202 0.000624 78.10 9,935,506 776,196,592

3 9,932,405 4,370 0.000440 77.15 9,930,220 766,261,086

4 9,928,035 3,256 0.000328 76.18 9,926,407 756,330,866

5 9,924,779 2,779 0.000280 75.21 9,923,390 746,404,459

6 9,922,000 2,461 0.000248 74.23 9,920,770 736,481,069

7 9,919,539 2,222 0.000224 73.25 9,918,428 726,560,299

8 9,917,317 2,063 0.000208 72.26 9,916,286 716,641,871

9 9,915,254 1,904 0.000192 71.28 9,914,302 706,725,585

10 9,913,350 1,903 0.000192 70.29 9,912,399 696,811,283

11 9,911,447 1,903 0.000192 69.30 9,910,496 686,898,884

12 9,909,544 2,140 0.000216 68.32 9,908,474 676,988,388

13 9,907,404 2,457 0.000248 67.33 9,906,176 667,079,914

14 9,904,947 2,932 0.000296 66.35 9,903,481 657,173,738

15 9,902,015 3,406 0.000344 65.37 9,900,312 647,270,257

16 9,898,609 3,880 0.000392 64.39 9,896,669 637,369,945

17 9,894,729 4,284 0.000433 63.41 9,892,587 627,473,276

18 9,890,445 4,757 0.000481 62.44 9,888,067 617,580,689

19 9,885,688 5,071 0.000513 61.47 9,883,153 607,692,622

20 9,880,617 5,237 0.000530 60.50 9,877,999 597,809,469

21 9,875,380 5,293 0.000536 59.54 9,872,734 587,931,470

22 9,870,087 5,261 0.000533 58.57 9,867,457 578,058,736

23 9,864,826 5,179 0.000525 57.60 9,862,237 568,191,279

24 9,859,647 5,078 0.000515 56.63 9,857,108 558,329,042

25 9,854,569 4,996 0.000507 55.66 9,852,071 548,471,934

26 9,849,573 4,964 0.000504 54.68 9,847,091 538,619,863

27 9,844,609 5,021 0.000510 53.71 9,842,099 528,772,772

28 9,839,588 5,185 0.000527 52.74 9,836,996 518,930,673

29 9,834,403 5,468 0.000556 51.77 9,831,669 509,093,677

30 9,828,935 5,829 0.000593 50.80 9,826,021 499,262,008

31 9,823,106 6,267 0.000638 49.82 9,819,973 489,435,987

32 9,816,839 6,754 0.000688 48.86 9,813,462 479,616,014

33 9,810,085 7,289 0.000743 47.89 9,806,441 469,802,552

34 9,802,796 7,862 0.000802 46.92 9,798,865 459,996,111

35 9,794,934 8,473 0.000865 45.96 9,790,698 450,197,246

36 9,786,461 9,111 0.000931 45.00 9,781,906 440,406,548

37 9,777,350 9,787 0.001001 44.04 9,772,457 430,624,642

38 9,767,563 10,490 0.001074 43.09 9,762,318 420,852,185

39 9,757,073 11,250 0.001153 42.13 9,751,448 411,089,867

40 9,745,823 12,085 0.001240 41.18 9,739,781 401,338,419

41 9,733,738 13,004 0.001336 40.23 9,727,236 391,598,638

42 9,720,734 14,046 0.001445 39.28 9,713,711 381,871,402

43 9,706,688 15,210 0.001567 38.34 9,699,083 372,157,691

44 9,691,478 16,543 0.001707 37.40 9,683,207 362,458,608

45 9,674,935 18,063 0.001867 36.46 9,665,904 352,775,401

46 9,656,872 19,787 0.002049 35.53 9,646,979 343,109,497

47 9,637,085 21,751 0.002257 34.60 9,626,210 333,462,518

48 9,615,334 23,952 0.002491 33.68 9,603,358 323,836,308

49 9,591,382 26,348 0.002747 32.76 9,578,208 314,232,950

50 9,565,034 28,858 0.003017 31.85 9,550,605 304,654,742

51 9,536,176 31,412 0.003294 30.95 9,520,470 295,104,137

52 9,504,764 33,951 0.003572 30.05 9,487,789 285,583,667

53 9,470,813 36,444 0.003848 29.15 9,452,591 276,095,878

54 9,434,369 39,058 0.004140 28.26 9,414,840 266,643,287

55 9,395,311 41,988 0.004469 27.38 9,374,317 257,228,447

56 9,353,323 45,438 0.004858 26.50 9,330,604 247,854,130

在文檔中 國立台灣大學電機資訊學院資訊工程學系 碩士論文 (頁 59-70)