题目
Over the next year, an operational process model predicts a 95% probability of no loss occurrence and a 5% probability of a single loss occurrence. If the single loss occurs, the severity is characterized by three possible outcomes: $10.0 million loss with 20% probability, $18.0 million loss with 50% probability, and $25.0 million loss with 30% probability. What is the model's one-year 90% expected shortfall (ES)?
选项
A.$9.25 million
B.$10.00 million
C.$13.88 million
D.$18.50 million
答案
A
解析
The 10% loss tail includes 5% of no loss (i.e., the 90% to 95% CDF) and 5% of the loss event.The average of this 10% tail is therefore given by:50% × 0 50% × [E (loss | loss event)] = 50% × [20% × 10 50% × 18 30% × 25] = $9.25 million10%的损失尾部包括5%的没有损失(即，即90%至95%的CDF)和5%的损失事件。因此，该10%尾部的平均值为:50% * 0 50% * [E(损失|损失事件)]= 50% *[20% * 10 50% * 18 30% * 25]= $ 925万