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Assume we have a risky event with a potential cost of damages, Xi, being lognormally distributed with mean = 7 variance = 5 :
Let us assume that an insurance covers n risky events. What is the expected value and standard deviation of X1 + X2 + ...+Xn if :
(iv) n = 10, correlation(Xi;Xj) = 0
(v) n = 100, correlation(Xi;Xj) = 0
这两小题的公式是什么？


(d) Suppose the insurance company needs to hold a risk margin on top of the central estimate of the insurance liability with respect to the portfolio of policies covering against this risky event, X1 + ...+Xn such that the probability of adequacy exceeds 0.75. How much provisions need to be held for the above cases?

我会用central limit theorem算sums &means， 但是前提是每个是independent的，如果有了correlation，公式是什么？

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关键词：correlation relation ATION Corr ATI insurance liability potential expected standard

这不是学术前沿吧……，而且correlation不是告诉了是0么，var(x+y)=var(x)+var(y)+2cov(x,y)=var(x)+var(y)

（iv）和（v) n = 10, correlation(Xi;Xj) = 0，前提是i不等于j，i等于j的时候就是方差。楼上把公式写给你了……不管独立条件有木有，这个var(x+y)=var(x)+var(y)+2cov(x,y)都是 成立的……