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这是一篇是用R语言计算精算现值和现值的方差
Individual Assignment I2AS 2021
1作业大纲
要求您计算精算现值和现值的方差，
以及刚刚购买的保险产品的两种不同的保费
投保人。保单持有人和保险产品的特征如下：
（1）保单持有人有自己的年龄和性别。
（2）她/他将获得40年的延期终生年金，并享有初始福利
每季度B欧元。随后的每笔付款将比付款的（τ/ 4）％大
前一个，其中τ表示年通货膨胀率。
（3）有年度保险费，最多可支付40年。第一溢价是
等于P，而第（k + 1）个溢价等于Pk + 1
=当k = 1、2、3，…时为P + k / 1000。 。 ..
（5）用于折现的实际年利率为i％。
（6）保单发行时的初始费用为第一笔给付金的一部分加上
首付保费的b％。
（7）在第一年没有更新费用。但是从第二个开始
年度续签费用等于当年保费的c％。
（8）在死亡的第二季度末发生的终端费为1,000欧元
自发行之日起每年以τ％的通胀率进行通胀。
自己选择B，τ，i，a，b和c的适当值。
2使用的死亡率分析定律
（a）威布尔（Weibull），形状参数γ= 1.1，比例参数λ=130。（姓氏
学生从A-F开始。）
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(b) Generalized DeMoivre, with α = 1/6 and ω = 120. (Last name of student G-L.)
(c) Gompertz, with B = 0.0003 and c = 1.07. (Last name of student M-S.)
(d) DeMoivre, for ω = 130. (Last name of student T-Z.)
3 Payment timing and frequency
(i) Use the quarterly benefits as indicated in the product description above. (Last name
of student starts with A-F.)
(ii) Instead of quarterly benefits, use monthly benefits. That is, replace ‘each quarter’
in bullet point (2) above by ‘each month’. Also replace τ/4 by τ/12. (Last name of
student starts with G-L.)
(iii) As in (ii), but now with ‘each 6 months’ to replace ‘each quarter’. Also replace τ/4
by τ/2. (Last name of student M-S.)
(iv) As in (ii), but now with ‘each week’ to replace ‘each quarter’. Also replace τ/4 by
τ/52. Assume 52 weeks in a year. (Last name of student T-Z.)
4 Assignment tasks
Here we formulate the assignment tasks in detail:
Tasks to perform: Determine P according to (i) the equivalence principle and (ii)
the portfolio premium principle (for which you choose α yourself).
Bonus task: For the value of P according to the equivalence principle, determine
the probability that the future loss is negative.
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Points of attention:
As mentioned above, you have to choose appropriate values of B, τ, i, a, b, c and α
yourself. Do this in such a way that the premiums exist.
If you feel that additional assumptions have to be made, then do so and clearly
explain and motivate this in your report.
You are allowed to obtain your answers analytically or numerically, whatever you
find convenient, but it is important that you carefully explain your methods (as
usual).