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程井井(￣▽￣) · 2020年11月15日

问一道题：NO.PZ2020011901000032 [ FRM I ]

  1. FRM I
  2. Financial Markets And Products

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.

为什么survival probability和death in1 year加起来不等于1呢
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1 个答案

品职答疑小助手雍 · 2020年11月15日

嗨，从没放弃的小努力你好：


这是个从最早开始不断累计计算的过程，我举个例子吧：用 活到71岁的概率 乘以 从71岁开始一年内不死亡的概率 得到 活到72岁的概率，即0.81525 x (1-0.017275) = 0.80117

这都是前面一年一年累计计算起来的结果。


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


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