保險精算課程設(shè)計

1、保險精算課程設(shè)計生命表的建立及其應(yīng)用姓 名： 學(xué) 號： 班 級： 專 業(yè)： 指導(dǎo)老師： 時 間： 摘要本文根據(jù)生命表的理論知識，完善已有部分?jǐn)?shù)據(jù)的生命表。并利用換算函數(shù)簡化生命保險和生命年金的一些復(fù)雜計算，根據(jù)換算公式同樣建立的生命表。并對完善好的生命表加以實踐應(yīng)用，通過舉例體現(xiàn)了生命表的重要作用。關(guān)鍵字：生命表 生存函數(shù) 換算函數(shù)目錄一、 生命表的發(fā)展史(1)二、 生命表的函數(shù)及其建立(1)三、 生命表的應(yīng)用(4)四、 參考文獻(xiàn)(6)五、 附件(6)一、 生命表的發(fā)展史生命表的建立可追溯到公元1661年，英國就有了歷史上最早的死亡機(jī)率統(tǒng)計表。到1693年，世界上第一張生命表是英國天文學(xué)家哈萊

2、制定了哈萊死亡表，它奠定了近代人壽保險費計算的基礎(chǔ)，到1700年，英國又建立了"均衡保費法"，使投保人每年繳費是同一金額。生命表是怎么來的呢？對于單個人來說，出生后何時死亡是不可知的，但對于一個國家，一個地區(qū)，在一定時間，一定的社會經(jīng)濟(jì)條件下，人的生、老、死是有規(guī)律可循的。人們可根據(jù)大數(shù)法則的原理，運(yùn)用統(tǒng)計方法和概率論，編制出生命規(guī)律的生命表，它是同批人從出生后，陸續(xù)死亡的生命過程的統(tǒng)計表。我國在1929-1931間，金陵大學(xué)的肖富德編制了中國第一張生命表，稱為"農(nóng)民生命表"。1982年第2次全國人口普查得到了完整的生命表資料，直到1995年末才制定出了

3、中國人壽保險業(yè)第一張經(jīng)驗生命表。二、 生命表函數(shù)及其建立2.1 生命表的概念生命表又稱“死亡表”（mortality table）,它是根據(jù)一定時期的特定國家（或）地區(qū)或特定人口群體（如壽險公司的全體被保險人、某企業(yè)的全體員工）的有關(guān)生存狀況統(tǒng)計資料，編制而成的統(tǒng)計表。生命表可以反應(yīng)出任意年齡的人在任何期限內(nèi)的生存概率、死亡概率等相關(guān)信息。2.2 生命表函數(shù)一個剛出生的個體（0歲），其未來生存時間可作為一個隨機(jī)變量，我們用表示。代表一個0歲的人未來生存的時間，也就是他的壽命。定義隨機(jī)變量的分布函數(shù)為：依定義，是一個0歲的人不晚于t歲死亡的概率。另一個補(bǔ)充性的概率也是經(jīng)常用到的，即一個0歲的人在

4、t歲之后死亡的概率，我們記作,稱為生存函數(shù)，即：定義：;。函數(shù)概念表示一個x歲的人在未來一年內(nèi)死亡的概率表示一個x歲的人在x+1歲仍然生存的概率x時刻死亡的人數(shù)在x時刻存活的人x歲的人的簡單生命期望值x歲的人的完全生命期望值主要公式;；; 表1 生命表函數(shù)2.3 換算函數(shù)為了計算各種類型的生命保險與生命年金的預(yù)期現(xiàn)值，我們將定義換算函數(shù)，這些函數(shù)可以把很長的計算大大簡化。主要換算函數(shù);表2 換算函數(shù)根據(jù)以上的換算函數(shù)，可以將原本復(fù)雜的計算簡化。以下是幾個主要的公式，用換算函數(shù)表示以達(dá)到簡化的目的。2.4 生命表的建立根據(jù)生命表6（1990-1993）養(yǎng)老業(yè)務(wù)男表給出的年齡和死亡率，根據(jù)以上公式

5、，在excel中，完善生命表。表3 完善后的生命表（全部數(shù)據(jù)見附件1）表4 換算函數(shù)表示的生命表（全部數(shù)據(jù)件附件2）三、生命表的應(yīng)用3.1 應(yīng)用一某人現(xiàn)在20歲，試求、及。根據(jù)兩全保險公式有：；根據(jù)延期的生命保險公式有:；根據(jù)標(biāo)準(zhǔn)永久遞增年金公式有：；所以通過查詢附件2中的生命表，易求得以上各值，結(jié)果分別如下：；3.2 應(yīng)用二現(xiàn)年35歲的人購買了一份終身壽險保單，保單規(guī)定：被保險人在10年內(nèi)死亡，給付金額為15 000元；10年后死亡，給付金額為20 000元。試求躉繳純保費。采用生命表6（1990-1993）養(yǎng)老業(yè)務(wù)男表計算，i=0.025。求解：躉交純保費為所以泵交純保費為：15000*0

6、.01563+20000*0.35529=7340.25。四、參考文獻(xiàn)1李曉林，壽險精算原理，北京：中國財政經(jīng)濟(jì)出版社（第二版），2012年。2吳嵐，黃海，何洋波，北京：金融數(shù)學(xué)引論（第二版），2005年。五、附件附件1：完善的生命表年齡死亡率qx生存率px生存人數(shù)lx死亡人數(shù)dxLxTx00.0027330.997267 100000027339986347541184674.4118574.9118510.0019410.998059 99726719369962997441184673.6157774.1157720.0014500.998550 99533114439946107341

7、457972.7589473.2589430.0011250.998875 99388811189933297241924771.8645972.3645940.0009000.999100 9927708939923237142535970.9455371.4455350.0007390.999261 9918767339915107043258970.0094470.5094460.0006210.999379 9911436169908366944071369.0612169.5612170.0005340.999466 9905285299902636844957068.1041368

8、.6041380.0004680.999532 9899994639897676745904267.1405167.6405190.0004210.999579 9895364179893276646904366.1719566.67195100.0003930.999607 9891193899889256547950765.1998265.69982110.0003890.999611 9887303859885386449038864.2254564.72545120.0004120.999588 9883464079881426350165763.2504563.75045130.00

9、04640.999536 9879394589877096251331262.2765262.77652140.0005430.999457 9874805369872126152537361.3054361.80543150.0006350.999365 9869446279866316053789360.3387360.83873160.0007310.999269 9863177219859575955094959.3770759.87707170.0008160.999184 9855968049851945856463258.4205158.92051180.0008830.9991

10、17 9847928709843575757903557.4682257.96822190.0009250.999075 9839229109834675659424356.5190157.01901200.0009440.999056 9830129289825485561032155.5713456.07134210.0009430.999057 9820849269816215462730954.6238555.12385220.0009270.999073 9811589109807035364522453.6754154.17541230.0009030.999097 9802498

11、859798065266406652.7252153.22521240.0008750.999125 9793648579789355168381751.7728652.27286250.0008510.999149 9785078339780905070445450.818251.3182260.0008330.999167 9776748149772674972594749.8614950.36149270.0008240.999176 9768598059764574874827348.9030649.40306280.0008260.999174 9760558069756514777

12、141447.9433948.44339290.0008400.999160 9752488199748394679535946.9830247.48302300.0008670.999133 9744298459740074582011146.0225246.52252310.0009060.999094 9735848829731434484568245.0624545.56245320.0009580.999042 9727029329722364387209844.1033244.60332330.0010220.998978 9717709939712744289939543.145

13、6143.64561340.0011000.998900 97077710689702434192762542.1897542.68975350.0011890.998811 96970911539691334095684841.2362141.73621360.0012920.998708 96855612519679313998713840.285340.7853370.0014090.998591 96730513639666243901858239.3374139.83741380.0015390.998461 96594214879651993805127738.3929238.89

14、292390.0016850.998315 96445516259636433708533537.452137.9521400.0018460.998154 96283017779619423612087936.5153137.01531410.0020250.997975 96105319469600803515804935.5828436.08284420.0022230.997777 95910721329580413419699634.6550435.15504430.0024420.997558 95697523379558063323788933.7322534.23225440.

15、0026830.997317 95463825619533573228091432.8148333.31483450.0029480.997052 95207728079506733132627631.9031132.40311460.0032410.996759 94927030779477323037420030.9974431.49744470.0035620.996438 94619333709445082942493030.0982230.59822480.0039170.996083 94282336939409762847873729.2058229.70582490.00430

16、60.995694 93913040449371082753591428.3206728.82067500.0047340.995266 93508644279328732659678427.4431427.94314510.0052050.994795 93065948449282372566169826.5736827.07368520.0057220.994278 92581552989231662473103925.7127226.21272530.0062920.993708 92051857929176222380522424.8606925.36069540.0069170.99

17、3083 91472663279115622288470624.0181124.51811550.0076040.992396 90839969079049452196998023.185423.6854560.0083590.991641 90149175368977232106158222.3630522.86305570.0091890.990811 89395682158898482016009021.5515622.05156580.0101000.989900 88574189468812681926613520.7514321.25143590.0111000.988900 87

18、679597328719291838039419.9631620.46316600.0121980.987802 867063105768617741750359919.1872419.68724610.0134030.986597 856486114798507461663653618.4241718.92417620.0147250.985275 845007124438387851578005017.6744718.17447630.0161750.983825 832564134678258311493504316.9386117.43861640.0177660.982234 819

19、097145528118211410247916.217116.7171650.0195090.980491 804545156967966971328338215.5104216.01042660.0214200.978580 788849168977804011247883714.8190415.31904670.0235130.976487 771952181517628771168998714.1434114.64341680.0258040.974196 753801194517440761091803513.4839713.98397690.0283110.971689 73435

20、0207907239551016423412.8411313.34113700.0310540.968946 71356022159702481942988412.2152612.71526710.0340520.965948 69140123544679629871632411.6067512.10675720.0373270.962673 66785724929655393802492311.0159211.51592730.0409010.959099 64292826296629780735706510.4430610.94306740.0448010.955199 616632276

21、2660281967141379.88840210.3884750.0490510.950949 5890062889157456160975059.3521919.852191760.0536800.946320 5601153006754508155084998.8345879.334587770.0587140.941286 5300483112151448749483848.3357298.835729780.0641850.935815 4989273202448291544183367.8556818.355681790.0701240.929876 466903327414505

22、3339194097.3944817.894481800.0765620.923438 4341623324041754234525066.9521157.452115810.0835320.916468 4009223349038417730183446.5285137.028513820.0910660.908934 3674323346135070226174226.1235586.623558830.0991960.900804 3339713312931740722499915.7370776.237077840.1079560.892044 30084332478284604191

23、60195.3688415.868841850.1173760.882624 2683653150025261516151775.0185835.518583860.1274860.872514 2368653019722176713468124.685985.18598870.1383130.861687 2066682858519237611099464.3706654.870665880.1498810.850119 178083266911647389032784.0722194.572219890.1622100.837790 151392245571391137251953.790

24、1754.290175900.1753160.824684 126835222361157175738023.5240154.024015910.1892100.810790 10459919791947034469683.2731713.773171920.2038950.796105 8480817292761623423693.0370143.537014930.2193680.780632 6751614811601102575622.8148413.314841940.2356170.764383 5270512418464961900462.6058493.105849950.25

25、26250.747375 4028710177351981373412.4090882.909088960.2703590.729641 30109814026039970542.2233992.723399970.2887840.711216 21969634418797669452.0472512.547251980.3078500.692150 15625481013220449761.8785222.378522990.3275000.672500 1081535429044293511.7140392.2140391000.3476690.652331 727325296009185

26、371.5487572.0487571010.3682800.631720 474417473871112641.3741891.8741891020.3892530.610747 29971167241465201.1753141.6753141030.4104970.589503 1830751145535220.9243881.4243881040.4319200.568080 107946684616920.568081.068081051.0000000.000000 61361330661311.5附件2：替換函數(shù)表示的生命表i=0.025年齡死亡率qxCxDxMxNxRxSx00

27、.0027332666.31000000.0172263.133937212.911344494.7926301442.710.0019411842.4972943.4169596.832937212.911172231.6892364229.820.0014501340.2947370.7167754.331964269.411002634.9859427016.930.0011251013.0922923.9166414.231016898.810834880.5827462747.540.000900789.7899400.6165401.230093974.910668466.4796

28、445848.750.000739632.1876674.3164611.529194574.310503065.2766351873.860.000621517.8854659.9163979.428317900.110338453.7737157299.570.000534434.1833296.7163461.627463240.210174474.3708839399.480.000468371.0812538.3163027.526629943.410011012.7681376159.390.000421325.4792349.3162656.525817405.19847985.

29、2654746215.8100.000393296.3772698.3162331.025025055.89685328.7628928810.7110.000389286.0753555.7162034.824252357.69522997.7603903754.9120.000412295.4734890.3161748.823498801.99360962.9579651397.3130.000464324.4716670.8161453.422763911.69199214.1556152595.5140.000543370.2698866.6161129.022047240.8903

30、7760.7533388683.9150.000635422.2681450.8160758.821348374.28876631.7511341443.1160.000731473.8664407.9160336.620666923.48715873.0489993068.9170.000816515.7647729.0159862.820002515.58555536.4469326145.5180.000883543.9631415.1159347.119354786.58395673.6449323630.0190.000925555.4615470.8158803.218723371

31、.58236326.5429968843.4200.000944552.5599903.8158247.718107900.78077523.4411245472.0210.000943537.9584719.5157695.217507996.97919275.6393137571.2220.000927515.4569920.2157157.316923277.37761580.4375629574.4230.000903489.4555504.2156641.916353357.27604423.1358706297.1240.000875462.2541466.0156152.5157

32、97852.97447781.2342352939.9250.000851438.2527797.3155690.315256387.07291628.7326555087.0260.000833418.1514485.9155252.114728589.77135938.5311298700.0270.000824403.2501519.4154833.914214103.86980686.4296570110.3280.000826394.0488884.0154430.813712584.46825852.5282356006.5290.000840390.6476566.1154036

33、.813223700.36671421.7268643422.1300.000867392.9464552.0153646.212747134.36517384.9255419721.8310.000906400.3452828.5153253.312282582.36363738.7242672587.5320.000958412.5441383.6152853.011829753.86210485.4230390005.2330.001022428.9430205.6152440.511388370.26057632.4218560251.4340.001100450.0419283.91

34、52011.610958164.65905191.8207171881.2350.001189474.0408607.5151561.610538880.75753180.3196213716.7360.001292501.9398167.5151087.610130273.25601618.7185674836.0370.001409533.3387954.2150585.79732105.85450531.1175544562.7380.001539567.5377958.6150052.49344151.65299945.3165812457.0390.001685605.2368172

35、.6149484.98966193.05149892.9156468305.4400.001846645.8358587.5148879.78598020.45000407.9147502112.4410.002025689.9349195.7148233.98239432.94851528.2138904091.9420.002223737.4339988.8147544.07890237.24703294.3130664659.0430.002442788.5330959.1146806.77550248.44555750.3122774421.7440.002683843.1322098

36、.4146018.27219289.34408943.7115224173.3450.002948901.4313399.2145175.16897190.94262925.5108004884.0460.003241963.9304854.0144273.76583791.74117750.4101107693.0470.0035621030.2296454.6143309.86278937.73973476.794523901.3480.0039171101.3288193.8142279.55982483.13830167.088244963.6490.0043061176.528006

37、3.3141178.25694289.43687887.482262480.4500.0047341256.5272056.0140001.75414226.03546709.276568191.1510.0052051341.4264164.0138745.25142170.13406707.571153965.0520.0057221431.2256379.5137403.74878006.13267962.366011794.9530.0062921526.6248695.1135972.54621626.63130558.661133788.8540.0069171627.024110

38、2.8134445.94372931.52994586.156512162.2550.0076041732.9233595.2132818.94131828.72860140.252139230.8560.0083591844.4226164.8131085.93898233.52727321.348007402.0570.0091891961.6218804.2129241.53672068.72596235.444109168.5580.0101002084.1211505.9127280.03453264.62466993.840437099.8590.0111002212.020426

39、3.2125195.93241758.62339713.836983835.2600.0121982345.2197069.1122983.93037495.52214518.033742076.6610.0134032483.4189917.3120638.62840426.32091534.130704581.2620.0147252626.1182801.8118155.32650509.01970895.527864154.8630.0161752772.9175717.1115529.22467707.21852740.225213645.8640.0177662923.316865

40、8.4112756.22291990.11737211.122745938.6650.0195093076.2161621.5109832.92123331.61624454.820453948.5660.0214203230.8154603.4106756.81961710.11514621.918330616.9670.0235133385.9147601.7103525.91807106.71407865.116368906.8680.0258043540.0140615.8100140.01659505.01304339.214561800.0690.0283113691.413364

41、6.296600.11518889.31204199.112902295.0700.0310543838.4126695.192908.71385243.11107599.111383405.7710.0340523978.8119766.689070.31258548.01014690.49998162.6720.0373274110.2112866.685091.51138781.4925620.18739614.6730.0409014229.9106003.680981.21025914.8840528.67600833.2740.0448014335.399188.276751.3919911.2759547.46574918.4750.0490514423.492433.672416.0820723.0682796.05655007.2760.0536804491.185755.867992.6728289.4610380.14834284.1770.0587144535.279173.163501.5642533.754