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Archie · 2022年05月05日

概率算了，不知道后面在干啥

  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.

就是不明白后面的计算过程，题也没搞懂

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1 个答案

品职答疑小助手雍 · 2022年05月05日

同学你好，概率算完，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。再折现求出PV。

设保费是X，第一年交X，第二年交保费的概率等于活到第二年的概率，也就是1-第一年去世的概率= 0.982725。这部分保费的pv要除以1.03。

所以X+ 0.982725X/1.03等于交的保费的现值，它应该等于第一步获得保费赔偿的期望的现值。

解出来X即可。

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