In this case, the 95% ES is the expected loss conditional on the loss occurring, which coincides with the mean of the normal distribution.

问题如下：

Assume that an operational process has a 5% probability of creating a material loss and, otherwise, no material loss is experienced (i.e., Bernoulli). If the material loss occurs, the severity is normally distributed with a mean of $4 million and standard deviation of $2 million. What is the 95% expected shortfall?

选项：

$0.71 million

$3.29 million

$4.00 million

$7.29 million

解释：

C is correct.

考点$：$Expected Shortfall

解析$：$ES = E(L | L >VaR). In this case, the 95% ES is the expected loss conditional on the loss occurring, which coincides with the mean of the normal distribution.

为何这里ES等于这个mean呢