壽險(xiǎn)精算課程設(shè)計(jì)

1、保險(xiǎn)精算課程設(shè)計(jì)題 目: 男性20年終身壽險(xiǎn) 按月繳均衡純保費(fèi) 學(xué) 院： 理學(xué)院 班 級(jí)： 數(shù)學(xué)13-2 學(xué) 生 姓 名： 吳迪 學(xué) 生 學(xué) 號(hào)： 2013027900 指 導(dǎo) 教 師： 陳輝 2016年 12 月 22 日課程設(shè)計(jì)任務(wù)書姓名吳迪班級(jí)數(shù)學(xué)13-2學(xué)號(hào)2013027900設(shè)計(jì)題目男性20年終身壽險(xiǎn)的按月繳均衡純保費(fèi)理論要點(diǎn)保費(fèi)支付方式是分期支付，終身壽險(xiǎn)換算公式，按月支付的終身生命年金，換算公式的求解。設(shè)計(jì)目標(biāo)通過數(shù)據(jù)的輸入，并借以Excel的計(jì)算，得出終身壽險(xiǎn)和按月支付的終身生命年金，進(jìn)而求出男性20年終身壽險(xiǎn)的按月繳均衡純保費(fèi)。研究方法步驟1.理解題意所求；2.計(jì)算相關(guān)換算公

2、式；3.求解按月繳納20年終身生命年金；4.求解20終身壽險(xiǎn)；5.求解20年終身壽險(xiǎn)按月繳均衡純保費(fèi)預(yù)期結(jié)果1. 求出相關(guān)換算函數(shù)；2. 利用Excel計(jì)算出均衡純保費(fèi)；3. 對(duì)結(jié)果進(jìn)行了合理的分析；計(jì)劃與進(jìn)步的安排課程設(shè)計(jì)安排兩周，分四個(gè)階段完成：第一階段（第1天）：上網(wǎng)搜查有關(guān)資料、確定了題目，錄入數(shù)據(jù)第二階段（第2-5天）：寫課程設(shè)計(jì)的前言、理論依據(jù)部分第三階段 (第6-12天)：寫設(shè)計(jì)的問題描述、用Excel進(jìn)行相關(guān)函數(shù)求解，并得出結(jié)果第四階段（第13-14天）：寫課程設(shè)計(jì)的結(jié)論以及最后的審核和排版、打印等摘要針對(duì)當(dāng)今保險(xiǎn)行業(yè)的均衡純保費(fèi)問題，本文借男性20年終身壽險(xiǎn)的按月繳均衡純保費(fèi)

3、問題展開論述，借助excel軟件和生命表去求解年繳費(fèi)12次的20年終身壽險(xiǎn)。對(duì)得出的結(jié)論進(jìn)行分析，對(duì)輸出結(jié)果進(jìn)行評(píng)價(jià)，并提出合理化的建議。關(guān)鍵詞 均衡純保費(fèi) 生命表 生命年金 目錄摘要.I1.問題的提出12.基本理論12.1 相關(guān)理論.12.2 相關(guān)公式. 12.3 符號(hào)說明.23.問題分析24.問題求解25.結(jié)論116.體會(huì).11.參考文獻(xiàn)11I1. 問題的提出當(dāng)今社會(huì)，在保費(fèi)支付方面有許多不同的保費(fèi)支付方式：如，在保單開始（生效）時(shí)一次性交付，這種保費(fèi)叫躉繳保費(fèi)，事實(shí)上，精算現(xiàn)值即可看作是相應(yīng)年險(xiǎn)或年金的躉繳凈保費(fèi)；更常見的保費(fèi)支付方式是分期支付。本文則借下題的研究來討論分期的保費(fèi)計(jì)算方法

4、。題：根據(jù)附錄表和4%的預(yù)定利率，計(jì)算死亡年末給付的20年終身壽險(xiǎn)的按月繳均衡純保費(fèi)。2. 基本理論2.1相關(guān)理論 保險(xiǎn)是一種分散風(fēng)險(xiǎn)的手段，他把大量的風(fēng)險(xiǎn)單位集合起來，形成風(fēng)險(xiǎn)集合，以收取保費(fèi)的方式建立準(zhǔn)備基金，當(dāng)個(gè)別風(fēng)險(xiǎn)單位發(fā)生保險(xiǎn)合同的保險(xiǎn)事故時(shí)，用保險(xiǎn)基金對(duì)保險(xiǎn)人進(jìn)行經(jīng)濟(jì)補(bǔ)償。因此，保險(xiǎn)人收取的保費(fèi)是風(fēng)險(xiǎn)準(zhǔn)備基礎(chǔ)，所以確定保費(fèi)是保險(xiǎn)公司正常運(yùn)營的前提，是以：在給定的條件（如生命表和預(yù)定利率）下，死亡年末給付的終身壽險(xiǎn)應(yīng)繳及收入與支出在精算上對(duì)等。利用精算等價(jià)原理確定純保費(fèi)，可以求出各種均衡純保費(fèi)。 在每個(gè)保單內(nèi)，保費(fèi)分m次繳付，并且死亡收益不作調(diào)整，那么其年保費(fèi)稱為真正分期保費(fèi)。對(duì)于1

5、單位的死亡年末給付的20年終身壽險(xiǎn)，每年支付m次的年保費(fèi)記作，稱為真正均衡年保費(fèi)。2.2 相關(guān)公式年繳保費(fèi)m次的n年定期保險(xiǎn) 終身壽險(xiǎn) 年支付m次的n年定期生命年金 相關(guān)換算函數(shù) 2.3相關(guān)符號(hào)說明：折現(xiàn)因子：年利率：死亡人數(shù)：生存人數(shù)：在死亡年末支付的定期保險(xiǎn)的精算現(xiàn)值：年支付m次的期初付的生命年金的精算現(xiàn)值 3.問題的分析有上述知識(shí)可得出，所求的男性20年終身壽險(xiǎn)的按月繳均衡純保費(fèi)為：。而 ,再借助Excel軟件，根據(jù)中國人壽保險(xiǎn)業(yè)經(jīng)驗(yàn)生命表求出，進(jìn)而求出，即男性20年終身壽險(xiǎn)的按月繳均衡純保費(fèi)。 4.問題求解借用excel軟件，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