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水瓶公主 · 2023年04月07日

幸存概率一般不用是吗

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.

一般只用存活概率是吗

1 个答案

品职答疑小助手雍 · 2023年04月07日

同学你好,因为这题问的是一个2年期的life insurance,所以只需要考虑近两年活着以及交保费的概率就可以了。survival那一列没用

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