Actuarial Notes

CAS Exam 7 Spring 2015, Question 6

Study guide: Exam 7

Given the following information for a book of workers compensation business:

Reported Losses ($000) – $250,000 Per-Occurrence Limit

Accident Year 12 Months 24 Months 36 Months 48 Months
2011 6,000 8,472 11,642 12,860
2012 5,620 8,748 12,156
2013 6,482 9,598
2014 6,216

Reported Losses ($000) – $1,000,000 Per-Occurrence Limit

Accident Year 12 Months 24 Months 36 Months 48 Months
2011 6,798 12,041 19,888 24,106
2012 5,823 10,541 17,896
2013 7,321 13,877
2014 6,984
Item Value
2014 earned premium $44,622,000
Expected loss ratio assumed in pricing 60%
Industry per-occurrence charge at $250,000 0.47
Industry per-occurrence charge at $1,000,000 0.05
Increased limit factor from basic limit to $250,000 1.21
Increased limit factor from basic limit to $1,000,000 2.27
  • Losses are fully developed at 48 months.
  • Ratio of reported losses limited to $250,000 per occurrence to reported losses limited to $1,000,000 per occurrence is given by y = (\text{ultimate ratio})\, e^{0.177t} where t is the time to ultimate maturity, measured in years.

Part a (0.5 points)

Using Siewert's loss ratio approach, estimate ultimate losses in the layer between $250,000 and $1,000,000 for accident year 2014.

Part b (1.25 points)

Using Siewert's implied development approach, estimate ultimate losses in the layer between $250,000 and $1,000,000 for accident year 2014.

Part c (1 point)

By adjusting the loss development factors for losses limited to $1,000,000 per occurrence to apply to losses in the layer between $250,000 and $1,000,000, calculate ultimate losses in the layer between $250,000 and $1,000,000 for accident year 2014.

Answer this question and see the worked solution

Concepts tested

More questions from this set