In Year 1 a risk has a Pareto distribution with [math]\alpha = 2[/math] and [math]\theta = 3000[/math] . In Year 2 losses inflate by 20%.
An insurance on the risk has a deductible of 600 in each year. [math]P_i[/math], the premium in year [math]i[/math], equals 1.2 times the expected claims.
The risk is reinsured with a deductible that stays the same in each year. [math]R_i[/math], the reinsurance premium in year [math]i[/math], equals 1.1 times the expected reinsured claims.
[math] \frac{R_1}{P_1} = 0.55 [/math]
Calculate [math]\frac{R_2}{P_2}[/math]
- 0.46
- 0.52
- 0.55
- 0.58
- 0.66
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
- Created by Admin, May 13'23
A primary insurance company has a 100,000 retention limit. The company purchases a catastrophe reinsurance treaty, which provides the following coverage
Layer 1: 85% of 100,000 excess of 100,000
Layer 2: 90% of 100,000 excess of 200,000
Layer 3: 95% of 300,000 excess of 300,000
The primary insurance company experiences a catastrophe loss of 450,000.
Calculate the total loss retained by the primary insurance company.
- 100,000
- 112,500
- 125,000
- 132,500
- 150,000
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
- Created by Admin, May 13'23
A primary liability insurer has a book of business with the following characteristics:
- All policies have a policy limit of 500,000
- The expected loss ratio is 60% on premiums of 4,000,000
A reinsurer provides an excess of loss treaty for the layer 300,000 in excess of 100,000. The following table of increased limits factors is available:
| Limit | ILF |
| 100,000 | 1.00 |
| 200,000 | 1.25 |
| 300,000 | 1.45 |
| 400,000 | 1.60 |
| 500,000 | 1.70 |
Calculate the reinsurer’s expected losses for this coverage (answer to the nearest 000s).
- 840,000
- 847,000
- 850,000
- 862,000
- 871,000
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
- Created by Admin, May 13'23