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YolandaQ · 2023年05月25日

为什么第二步算1.95X的时候

  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.

分母不是1.03的1.5次方或者二次方而是1.03的一次方

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1 个答案

DD仔_品职助教 · 2023年05月25日

嗨，爱思考的PZer你好：


同学你好，

请问说的是这一步吗？

这里交保费是0时刻和1时刻交，所以第二笔保费的PV是往前折现1期，也就是1次方

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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