保險精算課程設(shè)計

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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繁雜計算，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，通過舉例表達(dá)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、根據(jù)以上的換算函數(shù)，可以將原本繁雜的計算簡化。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。

AA1x:n1x:nx?nlvlx?nDx?nxxx?n?vnpx?v?x?lxvlxDx

??vk?1k|qx??vk?1k?0n?1dx?kMx?Mx?n?lxDx

Ax:nMx?Mx?n?Dx?n?Dxm|Ax?mExAx?m?Dx?mMx?mMx?m?

DxDx?mDx

Mx?kRx(IA)x??k|Ax???DxDxk?02.4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，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）

年齡01234567死亡率qx0.0027330.0019410.0014500.0011250.0009000.0007390.0006210.000534生存率px生存人數(shù)lx死亡人數(shù)dx0.997267100000027330.99805999726719360.99855099533114430.99887599388811180.9991009927708930.9992619918767330.9993799911436160.999466990528529Lx998634996299994610993329992323991510990836990263Tx7541184674411846734145797241924771425359704325896944071368449570ex74.4118573.6157772.7589471.8645970.9455370.0094469.0612168.10413e.x74.9118574.1157773.2589472.3645971.4455370.5094469.5612168.60413

表4換算函數(shù)表示的生命表（全部數(shù)據(jù)件附件2）

年齡01234567死亡率qx0.0027330.0019410.0014500.0011250.0009000.0007390.0006210.000534生存率px生存人數(shù)lx死亡人數(shù)dxCx0.997267100000027332666.30.99805999726719361842.40.99855099533114431340.20.99887599388811181013.00.999100992770893789.70.999261991876733632.10.999379991143616517.80.999466990528529434.1Dx1000000.0972943.4947370.7922923.9899400.6876674.3854659.9833296.7Mx172263.1169596.8167754.3166414.2165401.2164611.5163979.43163461.6NxRx33937212.911344494.732937212.911172231.631964269.411002634.931016898.810834880.530093974.910668466.429194574.310503065.228317900.110338453.727463240.210174474.3Sxiv926301442.70.0250.97561892364229.8859427016.9827462747.5796445848.7766351873.8737157299.5708839399.4三、生命表的應(yīng)用

3.1應(yīng)用一

某人現(xiàn)在20歲，試求A20:15、5|A20及(IA)20。根據(jù)兩全保險公式有：

A20:15=根據(jù)延期的生命保險公式有:

M20?M35?D35；

D20M255|A20?D20根據(jù)標(biāo)準(zhǔn)永久遞增年金公式有：

；

R20(IA)20=D20；

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：

A20:15=0.6923；5|A20=0.2595；(IA)20=13.4647

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15000元；10年后死亡，給付金額為20000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15000A35:10?2000010|A35

1A135:10??vk?09k?1kp35q35?k??vk?09k?135?kll35d35?k1?k?1??vd35?kl35?kl35k?0?1d)1044(1.025)??1111(d35?d?d?236337l351.025(1.025)(1.025)M35?M45151561.6-145175.1??0.01563D35408607.5

4

10|A35??vk?1070k?1kp35q35?k??vk?1070k?135?kll35d35?k1?l35?kl35k?10k?1v?d35?k701111?(d?d?d?114512461347l35(1.025)(1.025)(1.025)M45145175.1???0.35529D35408607.51?d)71105(1.025)所以泵交純保費為：。

5

15000*0.01563+20000*0.35529=7340.25

四、25262728293031323334353637383940414243444546474849505152530.0008510.0008330.0008240.0008260.0008400.0008670.0009060.0009580.0010220.0011000.0011890.0012920.0014090.0015390.0016850.0018460.0020250.0022230.0024420.0026830.0029480.0032410.0035620.0039170.0043060.0047340.0052050.0057220.0062920.9991490.9991670.9991760.9991740.9991600.9991330.9990940.9990420.9989780.9989000.9988110.9987080.9985910.9984610.9983150.9981540.9979750.9977770.9975580.9973170.9970520.9967590.9964380.9960830.9956940.9952660.9947950.9942780.9937089785079776749768599760559752489744299735849727029717709707779697099685569673059659429644559628309610539591079569759546389520779492709461939428239391309350869306599258159205188

8339780905070445450.818251.31828149772674972594749.8614950.361498059764574874827348.9030649.403068069756514777141447.9433948.443398199748394679535946.9830247.483028459740074582023146.0225246.522528829731434484568245.0624545.562459329722364387209844.1033244.603329939712744289939543.1456143.6456110689702434192762542.1897542.6897511539691334095684841.2362141.7362112519679313998713840.285340.785313639666243901858239.3374139.8374114879651993805127738.3929238.8929216259636433708533537.452137.952117779619423612087936.5153137.0153119469600803515804935.5828436.0828421329580413419699634.6550435.1550423379558063323788933.7322534.2322525619533573228091432.8148333.3148328079506733132627631.9031132.4031130779477323037420030.9974431.4974433709445082942493030.0982230.5982236939409762847873729.2058229.7058240449371082753591428.3206728.8206744279328732659678427.4431427.9431448449282372566169826.5736827.0736852989231662473103925.7127226.2127257929176222380522424.8606925.36069

54555657585960616263646566676869707172737475767778798081820.0069170.0076040.0083590.0091890.0101000.0111000.0121980.0134030.0147250.0161750.0177660.0195090.0214200.0235130.0258040.0283110.0310540.0340520.0373270.0409010.0448010.0490510.0536800.0587140.0641850.0701240.0765620.0835320.0910660.9930830.9923960.9916410.9908110.9899000.9889000.9878020.9865970.9852750.9838250.9822340.9804910.9785800.9764870.9741960.9716890.9689460.9659480.9626730.9590990.9551990.9509490.9463200.9412860.9358150.9298760.9234380.9164680.9089349147269083999014918939568857418767958670638564868450078325648190978045457888497719527538017343507135606914016678576429286166325890065601155300484989274669034341624009223674329

63279115622288470624.0181124.5181169079049452196998023.185423.685475368977232106158222.3630522.8630582158898482023009021.5515622.0515689468812681926613520.7514321.2514397328719291838039419.9631620.46316105768617741750359919.1872419.68724114798507461663653618.4241718.92417124438387851578005017.6744718.17447134678258311493504316.9386117.43861145528118211410247916.217116.7171156967966971328338215.5104216.01042168977804011247883714.8190415.31904181517628771168998714.1434114.64341194517440761091803513.4839713.98397207907239551016423412.8411313.3411322159702481235446796292492965539326296629780276266028192889157456130067545081311215144873202448291532741450533332404175423349038417733461350702942988412.2152612.71526871632411.6067512.10675802492311.0159211.51592735706510.4430610.9430667141379.88840210.388460975059.3521919.85219155084998.8345879.33458749483848.3357298.83572944183367.8556818.35568139194097.3944817.89448134525066.9521157.45211530183446.5285137.02851326174226.1235586.623558

83848586878889909192939495969798991001011021031041050.0991960.1079560.1173760.1274860.1383130.1498810.1622100.1753160.1892100.2038950.2193680.2356170.2526250.2703590.2887840.3078500.3275000.3476690.3682800.3892530.4104970.4319201.0000000.9008040.8920440.8826240.8725140.8616870.8501190.8377900.8246840.8107900.7961050.7806320.7643830.7473750.7296410.7112160.6921500.6725000.6523310.6317200.6107470.5895030.5680800.00000033397130084326836523686520666817808315139212683510459984808675165270540287301092196915625108157273474429971830107961333129317407324782846043150025261530197221767285851923762669116473824557139113222361157171979117292148111241810177814063444810354225291747116775146661394703761626011046496351982603918797132209044600938712414145584630622499915.7370776.23707719160195.3688415.86884116151775.0185835.51858313468124.685985.1859811099464.3706654.8706659032784.0722194.5722197251953.7901754.2901755738023.5240154.0240154469683.2731713.7731713423693.0370143.5370142575622.8148413.3148411900462.6058493.1058491373412.4090882.909088970542.2233992.723399669452.0472512.547251449761.8785222.378522293511.7140392.214039185371.5487572.048757112641.3741891.87418965201.1753141.67531435220.9243881.42438816926130.5680811.068081.5

附件2：替換函數(shù)表示的生命表i=0.025

年齡01死亡率qxCxDxMx172263.1169596.810

Nx33937212.932937212.9Rx11344494.711172231.6Sx926301442.7892364229.80.0027332666.31000000.00.0019411842.4972943.4234567891011121314151617181920212223242526272829300.0014501340.20.0011251013.00.0009000.0007390.0006210.0005340.0004680.0004210.0003930.0003890.0004120.0004640.0005430.0006350.0007310.0008160.0008830.0009250.0009440.0009430.0009270.0009030.0008750.0008510.0008330.0008240.0008260.0008400.000867789.7632.1517.8434.1371.0325.4296.3286.0295.4324.4370.2422.2473.8515.7543.9555.4552.5537.9515.4489.4462.2438.2418.1403.2394.0390.6392.9947370.7922923.9899400.6876674.3854659.9833296.7812538.3792349.3772698.3753555.7734890.3716670.8698866.6681450.8664407.9647729.0631415.1615470.8599903.8584719.5569920.2555504.2541466.0527797.3514485.9501519.4488884.0476566.1464552.0167754.3166414.2165401.2164611.5163979.4163461.6163027.5162656.5162331.0162034.8161748.8161453.4161129.0160758.8160336.6159862.8159347.1158803.2158247.7157695.2157157.3156641.9156152.5155690.3155252.1154833.9154430.8154036.8153646.211

31964269.431016898.830093974.929194574.328317900.127463240.226629943.425817405.125025055.824252357.623498801.922763911.622047240.821348374.220666923.420002515.519354786.518723371.518107900.717507996.916923277.316353357.215797852.915256387.014728589.714214103.813712584.413223700.312747134.311002634.910834880.510668466.410503065.210338453.710174474.310011012.79847985.29685328.79522997.79360962.99199214.19037760.78876631.78715873.08555536.48395673.68236326.58077523.47919275.67761580.47604423.17447781.27291628.77135938.56980686.46825852.56671421.76517384.9859427016.9827462747.5796445848.7766351873.8737157299.5708839399.4681376159.3654746215.8628928810.7603903754.9579651397.3556152595.5533388683.9511341443.1489993068.9469326145.5449323630.0429968843.4411245472.0393137571.2375629574.4358706297.1342352939.9326555087.0311298700.0296570110.3282356006.5268643422.1255419721.8

31323334353637383940414243444546474849505152535455565758590.0009060.0009580.0010220.0011000.0011890.0012920.0014090.0015390.0016850.0018460.0020250.0022230.0024420.0026830.0029480.003241400.3412.5428.9450.0474.0501.9533.3567.5605.2645.8689.9737.4788.5843.1901.4963.9452828.5441383.6430205.6419283.9408607.5398167.5387954.2377958.6368172.6358587.5349195.7339988.8330959.1322098.4313399.2304854.0296454.6288193.8280063.3272056.0264164.0256379.5248695.1241102.8233595.2226164.8218804.2211505.9204263.2153253.3152853.0152440.5152023.6151561.6151087.6150585.7150052.4149484.9148879.7148233.9147544.0146806.7146018.2145175.1144273.7143309.8142279.5141178.2140001.7138745.2137403.7135972.5134445.9132818.9131085.9129241.5127280.0125195.912

12282582.311829753.811388370.210958164.610538880.710130273.29732105.89344151.68966193.08598020.48239432.97890237.27550248.47219289.36897190.96583791.76278937.75982483.15694289.45414226.05142170.14878006.14621626.64372931.54131828.73898233.53672068.73453264.63241758.66363738.76210485.46057632.45905191.85753180.35601618.75450531.15299945.35149892.95000407.94851528.24703294.34555750.34408943.74262925.54117750.43973476.73830167.03687887.43546709.23406707.53267962.33130558.62994586.12860140.22727321.32596235.42466993.82339713.8242672587.5230390005.2218560251.4207171881.2196213716.7185674836.0175544562.7165812457.0156468305.4147502112.4138904091.9130664659.0122774421.7115224173.3108004884.0101107693.094523901.388244963.682262480.476568191.171153965.066011794.961133788.856512162.252139230.848007402.044109168.540437099.836983835.20.0035621030.20.0039171101.30.0043061176.50.0047341256.50.0052051341.40.0057221431.20.0062921526.60.0069171627.00.0076041732.90.0083591844.40.0091891961.60.0101002084.10.0111002212.0

60616263646566676869707172737475767778798081828384858687880.0121982345.20.0134032483.40.0147252626.10.0161752772.90.0177662923.30.0195093076.20.0214203230.80.0235133385.90.0258043540.00.0283113691.40.0310543838.40.0340523978.80.0373274110.20.0409014229.90.0448014335.30.0490514423.40.0536804491.10.0587144535.20.0641854552.90.0701244541.30.0765624498.10.0835324421.40.0910664309.80.0991964162.90.1079563981.60.1173763767.50.1274863523.60.1383133254.10.1498812964.5197069.1189917.3182801.8175717.1168658.4161621.5154603.4147601.7140615.8133646.2126695.1119766.6112866.6106003.699188.292433.685755.879173.172706.866380.660220.254253.348508.743015.837803.732900.128330.224115.620273.2122983.9120638.6118155.3115529.2112756.2109832.9106756.8103525.9100140.096600.192908.789070.385091.580981.276751.372416.067992.663501.558966.354413.549872.145374.040952.636642.932480.028498.424730.921207.317953.113

3037495.52840426.32650509.02467707.22291990.12123331.61961710.11807106.71659505.01518889.31385243.11258548.01138781.41025914.8919911.2820723.0728289.4642533.7563360.6490653.7424273.1364052.9309799.5261290.8218275.018