Revision as of 19:20, 5 August 2024 by Admin (Created page with "You are given: #The number of claims follows a Poisson distribution. #The number of claims and claim severity are independent. #The severity distribution is: {| class = "table table-bordered" | Claim Size | Probability |- | 5 | 0.60 |- | 40 | 0.35 |- | 60 | 0.05 |} Calculate the expected number of claims needed so the total cost of claims is within 5% of the expected with probability 0.90. <ul class="mw-excansopts"> <li>511</li> <li>726</li> <li>1083</li> <li>204...")
ABy Admin
Aug 05'24
Exercise
You are given:
- The number of claims follows a Poisson distribution.
- The number of claims and claim severity are independent.
- The severity distribution is:
| Claim Size | Probability |
| 5 | 0.60 |
| 40 | 0.35 |
| 60 | 0.05 |
Calculate the expected number of claims needed so the total cost of claims is within 5% of the expected with probability 0.90.
- 511
- 726
- 1083
- 2044
- 3126
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Aug 05'24
Key: D
For the severity distribution, we have [math] \mu_X = 20 [/math] and [math] \sigma_X^2 = 355 .[/math] The standard for full credibility is
[[math]]
\left( \frac{1.645}{0.05}\right)^2 (1 + CV_s^2) = \left( \frac{1.645}{0.05} \right)^2(1 + \frac{355}{20^2}) = 2043.05,
[[/math]]
round up to 2044.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.