寿险精算课程设计

1、保险精算课程设计题 目: 男性20年终身寿险 按月缴均衡纯保费 学 院： 理学院 班 级： 数学13-2 学 生 姓 名： 吴迪 学 生 学 号： 2013027900 指 导 教 师： 陈辉 2016年 12 月 22 日课程设计任务书姓名吴迪班级数学13-2学号2013027900设计题目男性20年终身寿险的按月缴均衡纯保费理论要点保费支付方式是分期支付，终身寿险换算公式，按月支付的终身生命年金，换算公式的求解。设计目标通过数据的输入，并借以Excel的计算，得出终身寿险和按月支付的终身生命年金，进而求出男性20年终身寿险的按月缴均衡纯保费。研究方法步骤1.理解题意所求；2.计算相关换算公

2、式；3.求解按月缴纳20年终身生命年金；4.求解20终身寿险；5.求解20年终身寿险按月缴均衡纯保费预期结果1. 求出相关换算函数；2. 利用Excel计算出均衡纯保费；3. 对结果进行了合理的分析；计划与进步的安排课程设计安排两周，分四个阶段完成：第一阶段（第1天）：上网搜查有关资料、确定了题目，录入数据第二阶段（第2-5天）：写课程设计的前言、理论依据部分第三阶段 (第6-12天)：写设计的问题描述、用Excel进行相关函数求解，并得出结果第四阶段（第13-14天）：写课程设计的结论以及最后的审核和排版、打印等摘要针对当今保险行业的均衡纯保费问题，本文借男性20年终身寿险的按月缴均衡纯保费

3、问题展开论述，借助excel软件和生命表去求解年缴费12次的20年终身寿险。对得出的结论进行分析，对输出结果进行评价，并提出合理化的建议。关键词 均衡纯保费 生命表 生命年金 目录摘要.I1.问题的提出12.基本理论12.1 相关理论.12.2 相关公式. 12.3 符号说明.23.问题分析24.问题求解25.结论116.体会.11.参考文献11I1. 问题的提出当今社会，在保费支付方面有许多不同的保费支付方式：如，在保单开始（生效）时一次性交付，这种保费叫趸缴保费，事实上，精算现值即可看作是相应年险或年金的趸缴净保费；更常见的保费支付方式是分期支付。本文则借下题的研究来讨论分期的保费计算方法

4、。题：根据附录表和4%的预定利率，计算死亡年末给付的20年终身寿险的按月缴均衡纯保费。2. 基本理论2.1相关理论 保险是一种分散风险的手段，他把大量的风险单位集合起来，形成风险集合，以收取保费的方式建立准备基金，当个别风险单位发生保险合同的保险事故时，用保险基金对保险人进行经济补偿。因此，保险人收取的保费是风险准备基础，所以确定保费是保险公司正常运营的前提，是以：在给定的条件（如生命表和预定利率）下，死亡年末给付的终身寿险应缴及收入与支出在精算上对等。利用精算等价原理确定纯保费，可以求出各种均衡纯保费。 在每个保单内，保费分m次缴付，并且死亡收益不作调整，那么其年保费称为真正分期保费。对于1

5、单位的死亡年末给付的20年终身寿险，每年支付m次的年保费记作，称为真正均衡年保费。2.2 相关公式年缴保费m次的n年定期保险 终身寿险 年支付m次的n年定期生命年金 相关换算函数 2.3相关符号说明：折现因子：年利率：死亡人数：生存人数：在死亡年末支付的定期保险的精算现值：年支付m次的期初付的生命年金的精算现值 3.问题的分析有上述知识可得出，所求的男性20年终身寿险的按月缴均衡纯保费为：。而 ,再借助Excel软件，根据中国人寿保险业经验生命表求出，进而求出，即男性20年终身寿险的按月缴均衡纯保费。 4.问题求解借用excel软件，求得，如下表： 表4-1xLx1.04(-x)dxDxDx+

6、2001000000130371000000447779.488419969630.9615384622150958618.2692430105.640629948130.9245562131603919760.5399413129.767839932100.8889963591242882960.0734396830.783549919680.854804191992847938.4038381185.351959909760.821927107813814510.0365366168.015869901630.790314526683782540.2017351752.0751798948

7、00.759917813587751923.4778337910.320689888930.730690205514722574.4289324616.307999883790.702586736463694421.9751311844.7236109879160.675564169432667400.6514299570.7424119874840.649580932426641450.7766287771.6004129870580.62459705452616513.5146276424.6753139866060.600574086509592529.9968265510.091814

8、9860970.577475083595569446.4467255008.2579159855020.555264503696547214.278244900.7109169848060.533908176799525795.9749235170.2878179840070.513373246893505162.8675225800.5413189831140.493628121964485292.7166216776.1747199821500.4746424241010466170.0568208082.072209811400.4563869461029447779.488419970

9、4.4117219801110.4388336021027430105.6406191629.7264229790840.4219553871009413129.7678183844.7385239780750.405726333981396830.7835176337.1604249770940.390121474950381185.3519169094.8901259761440.375116802922366168.0158162106.5778269752220.360689233902351752.0751155361.0772279743200.34681657892337910.

10、3206148847.8071289734280.333477471893324616.3079142556.2703299725350.320651415908311844.7236136476.8504309716270.308318668935299570.7424130600.0218319706920.296460258978287771.6004124916.4066329697140.285057941032276424.6753119417.2129339686820.2740941731100265510.0918114094.2004349675820.2635520911

11、82255008.2579108939.0456359664000.2534154711277244900.7109103944.0043369651230.2436687221386235170.287899101.65029379637370.2342968481508225800.541394404.98856389622290.2252854311646216776.174789847.23205399605830.2166206061798208082.07285422.12049409587850.2082890451966199704.411781123.690694195681

12、90.2002779282153191629.726476946.36739429546660.192574932358183844.738572885.03129439523080.1851682022584176337.160468935.15156449497240.1780463482831169094.890165092.55687459468930.1711984123102162106.577861353.48428469437910.1646138583398155361.077257714.91261479403930.1582825553723148847.80715417

13、4.37924489366700.1521947654076142556.270350729.82529499325940.146341124461136476.850447380.20053509281330.1407126154882130600.021844124.76498519232510.1353005925340124916.406640963.70329529179110.1300967235836119417.212937897.93702539120750.1250930036376114094.200434929.01604549056990.12028173369611

14、08939.045632059.23651558987380.1156555137594103944.004329291.71499568911440.111207224827799101.6502926630.0702578828670.106930023901494404.9885624078.59483588738530.10281733980689847.2320521642.08964598640470.0988628171065685422.1204919325.62443608533910.0950604011156681123.6906917134.46607618418250

15、.0914042321253776946.3673915073.88411628292880.0878886841356872885.0312913148.86829638157200.084508351466068935.1515611363.86375648010600.0812580291581365092.556879722.453322657852470.078132721702261353.484288227.151984667682250.0751276161828357714.912616879.019314677499420.0722380921959354174.37924

16、5677.509214687303490.0694597042093950729.825294620.189686697094100.0667881772231647380.200533702.649133706870940.0642194012370844124.764982918.579886716633860.0617494242509940963.703292259.659535726382870.0593744462647237897.937021715.963252736118150.0570908132780534929.016041276.172433745840100.054

17、8950132907132059.23651928.001779755549390.0527836663024529291.71499658.7108424765246940.0507535253129526630.0702455.5747305774933990.0488014673218824078.59483306.467568784612110.0469244873289221642.08964200.1299351794283190.0451196993337319325.62443126.5998725803949460.0433843263359817134.4660777.43

18、795689813613480.0417156983353815073.8841145.69240026823278100.0401112483316913148.8682925.95826265832946410.0385685083247511363.8637514.16974167842621660.037085104314479722.4533227.413218885852307190.035658754300908227.1519843.710515248862006290.034287263284196879.0193140871722100.032968522264655677

19、.5092140881457450.031700502242724620.1896860891214730.030481252218933702.649133090995800.029308896193982918.579886091801820.028181631168572259.659535092633250.027097722143461715.963252093489790.026055502119381276.172433094370410.0250533679697928.001779095273440.0240897767676658.7108424096196680.0231

20、632465908455.5747305097137600.0222723524415306.46756809893450.0214157233197200.129935109961480.0205920422237126.5998725010039110.01980004151177.43795689010124000.019038598245.69240026010214180.0183062561325.9582626501038050.01760216436714.1697416701044380.0169251572107.41321888501052280.016274192283

21、.7105152480 接上表 NxCxMxNxm24059057.362920.19230874648.072323600724.020.00316295723059057.361987.79585871727.8799922619690.650.00317103722100439.091425.06116369740.0841421678882.170.00321695921180678.551061.66680568315.0229720775988.510.00328817220297718.47815.351689967253.3561719909080.040.0033780241

22、9449780.07642.525709466438.0044819076462.970.00348272118635270.03519.023866465795.4787718276605.780.00359998317852729.83428.915150365276.454917508098.240.00372835817100806.35361.129582164847.5397516769626.410.00386696416378231.93312.786210264486.4101716059955.190.00401535415683809.95280.618962464173

23、.6239615377917.990.00417310215016409.3266.078343163893.00514722411.030.00433984714374958.52271.459486963626.9266514092389.830.00451498513758445.01293.934817263355.4671713486868.760.00469756713165915.01330.382379163061.5323512904918.720.00488662812596468.56371.600090362731.1499712345662.020.005081231

24、2049254.29410.185223462359.5498811808264.460.00528100911523458.31440.809912161949.3646611291925.330.00548616511018295.44457.555296861508.5547510795869.620.00569741510533002.73460.950815761050.9994510319341.450.00591617210066832.67451.559776660590.048639861600.4050.0061440389619053.183433.34818216013

25、8.488869421921.4310.0063828269188947.542409.377870359705.140678999596.3980.0066342028775817.774382.709166359295.76288593936.9980.006899728378986.991356.360962158913.053648204277.0380.0071807737997801.639332.555472858556.692687829974.6320.0074785297631633.623312.8285463582249220.00779396

26、47279881.548297.461904457911.308667125005.9840.0081278966941971.227286.341713357613.846756793188.7530.008481126617354.919279.953350557327.505046474426.0880.0088544546305510.196277.190340957047.551696168206.9390.0092486446005939.453278.786665456770.361355874044.1370.0096646135718167.853282.8651867564

27、91.574685591473.210.0101031655441743.178289.907298556208.70955320051.0520.0105654465176233.086299.537086455918.80225059354.3010.0110525574921224.828311.164957855619.265114808978.6690.0115657134676324.117324.735431255308.100154568537.7350.0121063034441153.829339.730429554983.364724337661.9140.0126758

28、074215353.288356.557518254643.634294115997.5410.0132759153998577.113374.503702354287.076773903206.1630.0139083293790495.041393.746405653912.573073698963.8520.0145750473590790.629414.61382553518.826673502960.3380.0152781713399160.903436.626620953104.212843314898.7310.016019863215316.165460.0717641526

29、67.586223134494.9660.0168025753038979.004484.662703952207.514462961477.180.0176288762869884.114510.632186151722.851752795585.2660.0185016182707777.536537.84412351212.219572636570.3760.0194238012552416.459566.621109150674.375442484194.5480.0203987152403568.652596.486404950107.754332338230.3620.021429

30、7772261012.382627.71897749511.267932198460.4920.0225208812124535.531660.537488548883.548952064677.1880.0236761221993935.51694.716499548223.011461936682.1570.0248998071869019.103730.042763547528.294961814286.2140.0261966911749601.89766.916331646798.25221697308.7150.0275720331635507.69805.078024646031

31、.335871585577.2940.0290312781526568.644844.507657945226.257841478927.6420.030580441422624.64885.059799844381.750191377203.050.0322260031323522.99926.795410343496.690391280254.0360.0339750461229118.001969.448784142569.894981187938.020.0358351151139270.7691012.96363341600.446191100118.9640.03781449810

32、53848.6481057482561016666.9570.039922103972724.95781101.86043639530.30121937457.87270.042167549895778.59041146.60929838428.44078862372.95110.044561278822893.55911191.24270837281.83148791298.28130.047114764753958.40761235.51270736090.58877724124.3190.049840321688865.85071278.82227534855.

33、07606660745.50370.052751136627512.36641320.72903733576.25379601059.69810.055861762569797.45381360.92397932255.52475544967.530.059187975515623.07461398.47763530894.60077492371.90460.062746474464893.24931433.12014829496.12314443177.3240.06655603417513.04871463.95534128063.00299397289.19810.07063620937

34、3388.28381490.2392226599.04765354613.25310.075008611332424.58051511.30801425108.80843315054.69270.079696665294526.64351526.35583523597.50042278517.51110.084725374259597.62741534.4739632207181070.090121687227538.39091535.04037220536.67062214113.02150.095915094198246.67591527.24189819001.

35、63024186041.22710.102136664171616.60571510.40539217474.38835160580.58310.108820058147538.01091484.07714515963.98295137618.71980.116001537125895.92121447.86511614479.90581117038.34340.123719333106570.29681401.56402813032.0406998716.999860.13201414989435.830741345.25104411630.4766782526.967190.1409294

36、0874361.946631279.2788410285.2256268335.381990.15051098561213.078331204.3387469005.94678156004.640780.16080715249849.214581121.3608267801.60803545393.090140.17186774540126.761261031.7037476680.24720936355.983270.18374546931899.60928936.93243355648.54346228746.725420.19649345725020.58996838.95378944711.61102822418.398240.21016715719343.08075739.84095023872.65723917225.493810.22482126114722.89106641.65966493132.81628913025.843540.24050774711020.24193546.66727782491.1566249682.5594810.2572828638101.662043456.78630141944.4893467065.9847560.2751901425842.00250