CAS Exam 8 Fall 2015, Question 14
Study guide: Exam 8
An insured has a large dollar deductible (LDD) policy. Total losses and ALAE limited to the deductible are distributed uniformly on the interval [0, 400,000], and total unlimited losses and ALAE are distributed uniformly on the interval [0, 800,000].
- The insured currently has an aggregate loss limit of $300,000.
- Credit risk is not contemplated in pricing.
- The deductible applies to both loss and ALAE.
The following expenses apply to this insured:
| Expense Item | Value | Applies to |
|---|---|---|
| ULAE | 7.5% | Loss & ALAE |
| Loss Based Assessments | 5% | Loss & ALAE |
| Overhead | $45,000 | Fixed |
| Acquisition | 6% | Written Premium |
| Commission | 12.5% | Written Premium |
| Premium Tax | 4% | Written Premium |
| Profit and Contingency | -5% | Written Premium |
Part a (2 points)
Calculate the LDD premium for this insured.
Part b (2 points)
It is later determined that, although the distribution of total unlimited losses and ALAE remains unchanged, the total losses and ALAE limited to the deductible actually follow the following distribution:
- 75% probability of loss and ALAE between $0 and $300,000
- 25% probability of loss and ALAE between $300,000 and $700,000
- Losses follow a uniform distribution within each range.
Use one or more Lee diagrams to demonstrate the impact to the premium for the LDD policy.
Answer this question and see the worked solution