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罗小胖 · 2023年10月04日

为什么，没懂

  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.

因为保费赔偿是1m，所以保费赔偿乘以概率等于就是期望获得的钱，这个应该如何理解

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1 个答案

pzqa27 · 2023年10月07日

嗨，从没放弃的小努力你好：


举个例子，比如我们玩抛硬币的游戏，正面向上可以获得100块，反面向上可以获得0元。那么我们预期可以获得的钱就是100*正面向上的概率。

这里同理，一旦被保人挂了，可以获得赔偿，没有挂，则没有赔偿，所以期望获得的钱就是保费赔偿乘以概率

----------------------------------------------
努力的时光都是限量版，加油！

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