The unlimited severity distribution for claim amounts under an auto liability insurance policy is given by the cumulative distribution:
The insurance policy pays amounts up to a limit of 1000 per claim.
Calculate the expected payment under this policy for one claim.
- 57
- 108
- 166
- 205
- 240
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
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.
An insurance company sells a policy with a linearly disappearing deductible such that no payment is made on a claim of 250 or less and full payment is made on a claim of 1000 or more.
Calculate the payment made by the insurance company for a loss of 700.
- 450
- 500
- 550
- 600
- 700
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
You are given the following loss data:
| Size of Loss | Number of Claims | Ground-Up Total Losses |
| 0 – 99 | 1100 | 58,500 |
| 100 – 249 | 400 | 70,000 |
| 250 – 499 | 300 | 120,000 |
| 500 – 999 | 200 | 150,000 |
| > 999 | 100 | 200,000 |
| Total | 2100 | 598,500 |
Calculate the percentage reduction in loss costs by moving from a 100 deductible to a 250 deductible.
- 25%
- 27%
- 29%
- 31%
- 33%
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
The graph of the density function for losses is:
Calculate the loss elimination ratio for an ordinary deductible of 20.
- 0.20
- 0.24
- 0.28
- 0.32
- 0.36
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Loss amounts have the distribution function
An insurance policy pays 80% of the amount of the loss in excess of an ordinary deductible of 20, subject to a maximum payment of 60 per loss.
Calculate the conditional expected claim payment, given that a payment has been made.
- 37
- 39
- 43
- 47
- 49
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
The random variable [math]X[/math] represents the random loss, before any deductible is applied, covered by an insurance policy. The probability density function of [math]X[/math] is
Payments are made subject to a deductible, [math]d[/math], where 0 < [math]d[/math] < 1.
The probability that a claim payment is less than 0.5 is equal to 0.64.
Calculate the value of [math]d[/math].
- 0.1
- 0.2
- 0.3
- 0.4
- 0.5
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
You are given the following information about a homeowners insurance policy:
- The deductible is 400 for claims up to 500.
- For claims of 500 or more, the deductible disappears linearly, until completely disappearing for claims of 2100 and beyond.
- There is no policy limit.
The policyholder submits a claim of X and receives a payment of 0.6X.
Calculate X.
- 618
- 808
- 1000
- 1300
- 1420
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.