为什么赔偿是在年中不是在年末

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：

18,153

17,874

17,996

17,767

解释：

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:

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

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.

这个0.5可以用1吗？

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1 个答案

pzqa27 · 2023年03月14日

嗨，努力学习的PZer你好：

这个是建模时的假设，因为这个人死是可能发生在某一年的任何一个时间段的，可能是3月挂了，也可能是11月死了，因此我们在决定保费的时候，不可能精准地估计到这个人什么时候死，只能假设他是在年中死去，这样算出来的均衡保费我们认为是比较合理的

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

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NO.PZ2020011901000032 问题如下 Whis the minimum USannupremium thinsurancompany shoulcharge for a two-yeterm life insuranpoliwith favalue of US1 million when the policyholr is a womage71? (Use Table 2.1 anassume interest rate of 3% compounannually.) A.18,153 B.17,874 C.17,996 17,767 The probability of a payout in the first ye(time 0.5 years) is 0.017275. The probability of a payout in the seconye(time 1.5 years) is (1 - 0.017275) * 0.019047 = 0.018718 The PV of the expectecost of the poliis therefore: 17,275/(1.030.5)+18,718/(1.031.5)=34,92817,275/(1.03^{0.5}) + 18,718/(1.03^{1.5}) = 34,92817,275/(1.030.5)+18,718/(1.031.5)=34,928The first premium is time zero. The seconpremium, time one year, ha probability of 1 - 0.017275 = 0.982725 of being ma. If the premium is X, the expectepresent value isX + 0.982725X/1.03 = 1.954102XThe minimum premium is given solving: 1.954102X = 34,928It 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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2022-05-05 04:53 1 · 回答

为什么赔偿是在年中不是在年末

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