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Stefanie🍅 · 2021年02月16日

解答看不懂

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020011901000032

问题如下：

What is the minimum USD annual premium that an insurance company should charge for a two-year term life insurance policy with face value of USD 1 million when the policyholder is a woman aged 71? (Use Table 2.1 and assume an interest rate of 3% compounded annually.)


选项：

A.

18,153

B.

17,874

C.

17,996

D.

17,767

解释：

B.

The probability of a payout in the first year (time 0.5 years) is 0.017275. The probability of a payout in the second year (time 1.5 years) is

(1 - 0.017275) * 0.019047 = 0.018718

The PV of the expected cost of the policy is therefore:

17,275/(1.030.5)+18,718/(1.031.5)=34,92817,275/(1.03^{0.5}) + 18,718/(1.03^{1.5}) = 34,928

The first premium is at time zero. The second premium, at time one year, has a probability of 1 - 0.017275 = 0.982725 of being made. If the premium is X, the expected present value is

X + 0.982725X/1.03 = 1.954102X

The minimum premium is given by solving:

1.954102X = 34,928

It is 17,874.

 1 解答的第一部分（1-0.o19047)*0.019047 是在算保人第一年没死但是第二年死的概率，我理解的对吗？ 2 这里的pv of expected cost是在算什么？为什么是17275除以年利率（1.03)^0.5?  0.017275为什么会乘以100万？ 3 然后之后的解答也不理解，为什么要设X，这个不是一个两年的保单吗？如果投保人在两年内挂了就有100万可以拿，如果过了两年没挂就什么也拿不到。
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1 个答案

品职答疑小助手雍 · 2021年02月18日

嗨，从没放弃的小努力你好：


1.可能你打错数字了哈，(1 - 0.017275) * 0.019047 = 0.018718是在算保人第一年没死但是第二年死的概率的~

2.因为第一年死了的话，理赔金额是1million（题目中提到过），所以理赔的期望就是理赔金额乘以概率。除以利率是折现的过程。

3.这就要理解题意了，这样才能理解这个X + 0.982725X/1.03 = 34,928是怎么来的。这题最终的意义其实是：保险公司（第一年没死的话）这两年收相同的金额X，所以等号左边是第一年交的X和第一年活下来的话第二年期望缴费的概率0.982725乘以X，等号右边是死亡需要赔付保费的期望的现值。两边要相等。


-------------------------------
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