ABy Admin
May 14'23

Exercise

The random variable for a loss, X, has the following characteristics:

[math]x[/math] [math]F(x)[/math] [math]\operatorname{E}( X \wedge x ) [/math]
0 0.0 0
100 0.2 91
200 0.6 153
1000 1.0 331


Calculate the mean excess loss for a deductible of 100.

  • 250
  • 300
  • 350
  • 400
  • 450

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

ABy Admin
May 14'23

Key: B

Mean excess loss =

[[math]] \frac{\operatorname{E}(X) - \operatorname{E}(X \wedge 100)}{1-F(100)} = \frac{331-91}{0.8} = 300 [[/math]]

Note that [math]\operatorname{E}( X ) = \operatorname{E}( X \wedge 1000)[/math] because [math]F(1000) = 1.[/math]

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

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