Revision as of 13:38, 14 May 2023 by Admin (Created page with "For an aggregate loss distribution S: #The number of claims has a negative binomial distribution with <math>r = 16</math> and <math>\beta = 6</math> . #The claim amounts are...")
ABy Admin
May 14'23
Exercise
For an aggregate loss distribution S:
- The number of claims has a negative binomial distribution with [math]r = 16[/math] and [math]\beta = 6[/math] .
- The claim amounts are uniformly distributed on the interval (0, 8).
- The number of claims and claim amounts are mutually independent.
Calculate the premium such that the probability that aggregate losses will exceed the premium is 5% using the normal approximation for aggregate losses.
- 500
- 520
- 540
- 560
- 580
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
May 14'23
Key: D
We have the following table:
| Item | Dist | E() | Var() |
|---|---|---|---|
| Number claims | NB(16,6) | 16(6) = 96 | 16(6)(7) = 672 |
| Claim amounts | U(0,8) | (8 − 0)2 / 12 = 5.33 | |
| Aggregate | 4(96) = 384 | 96(5.33) + 672(42 ) = 11, 264 |
Premium = [math]\operatorname{E}(S ) + 1.645 \sqrt{\operatorname{E}[S )} = 384 + 1.645 \sqrt{11,264} = 559 [/math]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.