保险数理与经营概述

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,第五章保险数理与经营概述,本章重点：,1.保险费、保险费率及保险责任准备金的含义与构成,2.保险费率的计算原理,3.保险经营的主要环节,第一节保险费率的构成与厘定,一、概述（P98）,（一）保险费的构成,保险费（,毛保费或营业保费,）纯保费附加保费,纯保费：毛保费中用于支付保险金的部分,附加保费：毛保费中对应营业费用、营业税金和营业利润的部分,（二）保险费率的含义与构成,1.概念：保险费与保险金的比率（,单位保额对应的保险费额,）,2.构成：保险费率（,营业费率或毛费率,）纯费率附加费率,保险费保险金保险费率,二、保险费率的厘定原则与方法,（一）基本原则,适当性、公正合理性、稳定性、灵活性、促进防损原则,（二）一般方法,分类法（综合法）：分类搜集资料综合计算风险概率,观察法（判断法或个别法）：对个案单独估计出险率,修正法：利用数理方法或经验进行费率修正,基础是,分类法（综合法）,三、非寿险费率的厘定,（,P101,）,非寿险：产险、意外伤害险及健康险,（一）确定纯费率：即纯保费与保险金之比,基本原理：,收支平衡原则,纯保费收入赔款支出,即承保金额纯费率赔款支出,纯费率赔款支出承保金额,即,保额损失率,例如：某市私家车保有量50万辆，车均价值10万元，若承保率8成，则保险公司承保总金额400亿元。一年后所有合同共理赔4亿元，意味着车险业务每承保100元钱平均支付赔款1元钱，即保额损失率为1/100,计算保额损失率及其均值,保额损失率x 每一年的赔款金额承保总额,计算保额损失率的均方差（标准差）：衡量保额损失率的变动幅度,计算稳定系数（保额损失率的相对变动率）：用以决定均方差的附加次数,V,x,若,V,在10以下，则附加一个均方差；在1020之间，则附加两个；若大于20，则附加三个,纯费率平均保额损失率附加均方差,平均保额损失率（稳定系数）,（二）确定附加费率,1.定义：附加保费与保险金之比,2.计算,理论算法：,营业费率营业税率营业利润率,经验算法：,纯费率附加保费占纯保费的比例,（三）确定毛费率,毛费率纯费率附加费率,四、寿险费率的厘定（,P104,）,（一）寿险保费的分类,1.按组成分：纯保费与附加保费,2.按交费方式分,趸交保费：一次性交清的保费,均衡保费：分期交纳且每次交费额均相等的保费,自然保费：随生死概率变动而相应交纳的保费,（二）计算原则：收支平衡收入（,保费,）与支出（,给付额,）在,精算现值上,的相等,精算现值：既考虑折现率又考虑生死概率的折现值,公式：纯保费精算现值附加保费精算现值保险金精算现值各项税、利、费精算现值,（三）计算基础,三要素：预定死亡率，预定利息率（收益率、折现率），预定费用率,1.人的生死概率,0 1040 ,年龄,终极年龄,死亡率,由生命表（生命函数）来反映,简单生命函数,x：年龄 l：生存 d：死亡,l,x,：x岁的人在年初的生存人数,d,x,：x岁的人在年内死亡的人数,d,x,l,x,l,x1,p,x,：x岁的人在年内的生存概率,p,x,l,x1,l,x,q,x,：x岁的人在年内的死亡概率,q,x,d,x,l,x,p,x,q,x,1,n,p,x,：x岁的人在n年内的生存概率,n,q,x,：x岁的人在n年内的死亡概率,n,p,x,n,q,x,1,中国人寿保险业经验生命表死亡率数据节选,年龄,19901993生命表,20002003生命表,非养老金业务男表,非养老金业务女表,养老金业务男表,养老金业务女表,非养老金业务男表,非养老金业务女表,养老金业务男表,养老金业务女表,25,0.000945,0.000519,0.000851,0.000467,0.000661,0.0003,0.000575,0.000261,26,0.000925,0.000520,0.000833,0.000468,0.000692,0.000315,0.000601,0.000274,27,0.000915,0.000525,0.000824,0.000473,0.000716,0.000328,0.000623,0.000285,28,0.000918,0.000533,0.000826,0.000480,0.000738,0.000338,0.000643,0.000293,29,0.000933,0.000546,0.000840,0.000491,0.000759,0.000347,0.00066,0.000301,30,0.000963,0.000566,0.000867,0.000509,0.000779,0.000355,0.000676,0.000308,31,0.001007,0.000592,0.000906,0.000533,0.000795,0.000362,0.000693,0.000316,32,0.001064,0.000625,0.000958,0.000563,0.000815,0.000372,0.000712,0.000325,33,0.001136,0.000666,0.001022,0.000599,0.000842,0.000386,0.000734,0.000337,34,0.001222,0.000714,0.001100,0.000643,0.000881,0.000406,0.000759,0.000351,35,0.001321,0.000772,0.001189,0.000695,0.000932,0.000432,0.000788,0.000366,36,0.001436,0.000838,0.001292,0.000754,0.000994,0.000465,0.00082,0.000384,37,0.001565,0.000914,0.001409,0.000823,0.001055,0.000496,0.000855,0.000402,38,0.001710,0.001001,0.001539,0.000901,0.001121,0.000528,0.000893,0.000421,39,0.001872,0.001098,0.001685,0.000988,0.001194,0.000563,0.000936,0.000441,40,0.002051,0.001208,0.001846,0.001087,0.001275,0.000601,0.000985,0.000464,2.,利息的度量,（1）三要素：本金P，利率i，期间n,（2）单利计算,终值SP（1ni）,现值P S（1ni）,（3）复利计算,终值SP（1i）,n,现值P S（1i）,n,SV,n,其中：V1（1i）,寿险精算需考虑生死概率,3,.,预定费用率（略）,年金终值系数公式：,年金现值系数公式：,（四）纯保费的计算,1.趸交纯保费：以n年期定期生存保险为例,l,40,=,966271人,2.期交纯保费：以n年期定期死亡保险为例,结论：趸交纯保费现值年交纯保费现值支付的保险金现值,寿险保费与利率高低成反向关系,补充：传统分红保险的红利来源（以死亡保险为例）,死差益预定死亡率高于实际死亡率的差额,利差益预定利息率低于实际利息率的差额,费差益预定费用率高于实际费用率的差额,反之则叫差损,（五）营业保费（,毛保费,）的计算,1.附加费用的构成：新合同费，保单维持费，收费费用,2.计算,（1）固定比例法：认为附加费是毛保费的一定比例，即PPkPP：毛保费，P：纯保费,故PP（1k）,（2）比例常数法：认为有一个固定费用支出,即PPkP,故P（P）（1k）,（3）三元素法：分别计算三项附加费用,第二节保险责任准备金概述,一、含义与类型（P121）,（一）责任准备金是保险企业为履行将来的保险金赔付责任而提存的货币准备,简单讲，主要是指保险人尚不能算作自己利润的收入,（二）分类,1.按来源分：保费准备金与非保费准备金,2.按性质分：法定准备金与任意准备金,3.按业务分：非寿险准备金与寿险准备金,二、非寿险责任准备金的提存,（一）未到期责任准备金：源于会计年度与保单年度的不一致性,1.按自留保费来提取,自留保费全年保费收入分入保费分出保费,2.假定保费收入的时刻T服从均匀分布,3.四种估算周期（P123）,（1）年平均估算法（1/2法）,年末未到期责任准备金当年自留保费50%,（2）季平均估算法（1/8法）,年末未到期责任准备金1季度保费 l8十2季度保费38十3季度保费58十4季度保费78,（3）月平均估算法（1/24法）,年末未到期责任准备金=1月保费1/24+2月保费3/24+3月保费5/24+12月保费23/24,（4）日平均法,年末未到期责任准备金=首日保费1/730+次日保费3/730+年末最后一日保费729/730,（二）未决赔款准备金,含义：年终决算前已经发生事故但未决定赔付额或应付未付的赔款准备金,包括：未报未决、已报未决和已决未付赔款准备金,（三）总准备金（,保险保障基金,）,是保险人为应付巨灾损失而从保费或税后利润中提存的准备金,（四）其他：如长期健康险责任准备金,三、寿险责任准备金的提存,（一）,寿险责任准备金提存的原因,1.,保费的平准化,2.保费交付期与保单责任期不相等：例如趸交保费,3.储蓄性业务的存在：例如投资分红保险,（二）寿险责任准备金的提取方式,1.,理论责任准备金：以理论上的均衡纯保费为基础,2.,实际责任准备金：以修正后（扣除代理人佣金）的非均衡纯保费为基础,均衡纯保费,均衡附加保费,自 然保费,均衡总保费,修正后附加保费,修正后纯保费,自 然保费,均衡总保费,3.二者的关系,以终身死亡保险为例,（三）寿险责任准备金的计算,1.,理论责任准备金的计算,依据保险人的收支平衡原则，任何时点均有：,已收均衡纯保费的精算积存值未来应收均衡纯保费的精算现值已付保险金的精算积存值未来应付保险金的精算现值,移项后：,已收均衡纯保费的精算积存值-已付保险金的精算积存值未来应付保险金的精算现值-未来应收均衡纯保费的精算现值,等号前为,过去法（追溯法）,，后为,未来法（预期法）,2.,实际责任准备金的计算,（1）完全初年度定期制修正法（FPT）法,自 然保费,让首年度纯保费与自然保费相等，即首年责任准备金为0,调高以后年度的纯保费，使得责任准备金相应较高,调高以后年度的纯保费，使得责任准备金相应较高,调高以后年度的纯保费，使得责任准备金相应较高,（,2）,其他修正法,（P129）：思路与FPT大体一致,第三节保险经营管理原理,一、保险经营的特征（P130）,例如：利润形成的特殊性,普通工业企业：净利润（主营收入其他业务收入）（生产成本期间费用其他业务支出税收）,保险企业：净利润（保费收入其他业务收入,转回的责任准备金,投资利润,）,（赔款支出,责任准备金,各项费用税收）,二、保险经营的环节,（一）保险展业,1.含义：保险公司为推广和扩展业务而进行的各项市场活动,狭义仅指保单推销广义保险市场营销,2.方式,保险人展业（,直销,）；代理人展业（,营销,）；经纪人展业,（二）保险承保,1,.含义：对投保要约进行审核以决定是否承诺的过程,2.内容,（1）承保审核（核保）：审核主体资格；保险标的；保额、保费与责任,（2）承保控制,A.防止逆选择（adverse selection）,含义：因为信息不对称，投保方对投保及退保与否所做出的不利于保险人的选择,表现：不实告知；带病投保；低危不参保等,应对：规定告知与保证义务；统括承保；差别费率等,B.防止道德风险（moral hazard）,含义：特指因信息不对称所诱发的投保方在合同履行期间的失德性行为,表现：谎报事故；夸大事故损失；放任损失扩大；故意诈保,应对：限制保额；实行共保（,免赔额与自负额,）；处罚与激励并举：规定保险诈骗罪、实行无赔款优待等,（三）保险的防灾防损（P138）：预防风险与灾害,（四）保险理赔,1.含义：保险人或