这个作业是用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。)
3
(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.
4
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).


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