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黄石2024-10-29 09:45:07
同学你好。probability that the person will live until 72 and die at the age of 72 = probability that the person will live until 72 × probability that the person will die at the age of 72。其中,probability that the person will die at the age of 72可直接从表格中获得(0.018861),probability that the person will live until 72实为P(活到72岁|活到70岁),是一个条件概率(因为这个投保人当前70岁,这是一个条件)。P(活到72岁|活到70岁) = P(活到72岁 & 活到70岁)/P(活到70岁),其中P(活到72岁 & 活到70岁) = P(活到72岁),这两件事同时发生的概率就是这个人活到72岁的概率(他只要活到72岁那就必然活到了70岁)。根据题目信息,P(活到72岁|活到70岁) = P(活到72岁)/P(活到70岁) = 0.79911/0.82573。
这道题其实直接用课上教的方法解即可:收到payoff的概率 = 70岁这年没死的概率*71岁这年没死的概率*72岁这年死了的概率 = (1 - 0.015413)*(1 - 0.017089)*0.018861 = 0.01825。0.01825*350,000 = 6388.53。
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讲得很清晰,谢谢


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