| 利用数学建模原理探索保险产品的设计方案 |
| |
| 引用本文： | 张明会,高婷婷.利用数学建模原理探索保险产品的设计方案[J].洛阳师范学院学报,2014(11):16-20. |
| |
| 作者姓名： | 张明会 高婷婷 |
| |
| 作者单位： | 陇南师范高等专科学校数信学院,甘肃成县,742500 |
| |
| 摘 要： | 在考虑保险公司不盈不亏的前提下,当银行利率为复利率时,利用等比数列的求和公式,建立了月保险费a,保险金交纳年限n,固定工资b,死亡年限m(m>n)及银行利率c之间的指数模型:b(1+c)12n+a(1+c)12(m+n)-(a+b)(1+c)12m=0利用以上公式给出了在a,n,m,c已知的情况下b的计算公式:b=(1+c)12(m+n)-(1+c)12m(1+c)12m-(1+c)12na.由题目所给数据:a=1000,n=20,m=80,c=0.25%,运用Excel办公软件,计算出了固定工资b=983.73元.同时给出了n和m的关系式:m=n-ln a+b-a(1+c)12()n12ln(1+c)+lnb12ln(1+c).在a=1000,b=2000,c=0.25%时,运用MathCAD数学工具软件绘出了函数图象,并利用Excel计算出了n和m的一些数值解,很好的解决了题目所提的问题,并利用函数图象对保险公司的盈亏区域进行了讨论.
|
| 关 键 词： | 指数模型 等比数列 求和公式 复利率 |
Design Scheme of Insurance Products on the Basis of Mathematical Modeling Principle |
| |
| ZHANG Ming-hui,GAO Ting-ting.Design Scheme of Insurance Products on the Basis of Mathematical Modeling Principle[J].Journal of Luoyang Teachers College,2014(11):16-20. |
| |
| Authors: | ZHANG Ming-hui GAO Ting-ting |
| |
| Institution: | (Mathematics Department, Longnan Teachers＇ College, Cheng County 742500, China) |
| |
| Abstract: | Under the premise that the insurer generates neither profit nor loss, when bank interest is compound interest, using the summation formula of geometric series, this paper establishes the exponential model ofmonthly premium a, premium paying period n, fixed wage b, age at death m and bank interest c. b（1＋c）12n ＋a（1＋c）12（m＋n）-（a＋b）（1＋c）12m =0 Given the above formula, with a, n, m, c known, the formula to calculate b is： b=（1＋c）12 m＋n -（1＋c）12m /（1＋c）12m -（1＋c）12n a Given the data in the question： a = 1000, n = 20, m = 80, c = 0.25%, using Excel to calculate the fixed wage ： b = 983.73.Formula of relation between n and m： m=n-ln a＋b-a（1＋c）12n）/12ln（1＋c）＋ lnb/12ln（1＋c） Given a = 1000, b = 2000, c = 0.25%, the function is graphed with MathCAD, and some numerical solutionsof n and m are calculated with Excel, a good solution to the question is given, and the profit-loss margin of the in-surer is discussed with the function graph. |
| |
| Keywords: | exponential model geometric series sum formula compound interest |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
