Actuarial Notes

CAS Exam 5 Fall 2015, Question 19

Study guide: Exam 5

An actuary has performed a reserve analysis on a line of business using four techniques. The data, techniques, and assumptions are as follows:

Reported Claims ($000) as of (months):

Accident Year 12 24 36 48 60
2010 5,000 8,500 11,000 11,500 11,500
2011 6,000 10,800 13,000 13,800
2012 7,000 12,300 15,300
2013 8,000 14,000
2014 10,000

Reported Claim Age to Age Factors:

Accident Year 12-24 24-36 36-48 48-60 60-Ult
2010 1.70 1.29 1.05 1.00
2011 1.80 1.20 1.06
2012 1.76 1.24
2013 1.75
Selected 1.75 1.25 1.05 1.00 1.00
CDF to Ultimate 2.29 1.31 1.05 1.00 1.00

Paid Claims ($000) as of (months):

Accident Year 12 24 36 48 60
2010 1,100 4,500 8,100 10,000 11,000
2011 1,400 5,500 9,300 11,700
2012 1,600 6,400 11,200
2013 1,800 7,200
2014 1,800

Paid Claim Age to Age Factors:

Accident Year 12-24 24-36 36-48 48-60 60-Ult
2010 4.09 1.80 1.23 1.10
2011 3.93 1.69 1.26
2012 4.00 1.75
2013 4.00
Selected 4.00 1.75 1.25 1.10 1.00
CDF to Ultimate 9.68 2.42 1.38 1.10 1.00

Ratio of Paid Claims to Reported Claims as of (months):

Accident Year 12 24 36 48 60
2010 22% 53% 74% 87% 96%
2011 23% 51% 72% 85%
2012 23% 52% 73%
2013 23% 51%
2014 18%

Projected Ultimate Claims:

Accident Year Earned Premium ($000) Development Techniques — Reported ($000) Development Techniques — Paid ($000) Bornhuetter-Ferguson Techniques — Reported ($000) Bornhuetter-Ferguson Techniques — Paid ($000)
2010 18,800 11,500 11,000 11,500 11,000
2011 23,200 13,800 12,870 13,800 13,071
2012 25,900 16,065 15,456 16,102 15,836
2013 31,700 18,340 17,424 18,876 19,291
2014 30,000 22,900 17,424 20,985 19,286
  • Selected expected claim ratio used in Bornhuetter-Ferguson Techniques is 65%.
  • Claims ratio trend is 0%.
  • There is no reported development beyond 60 months.

Part a (1 point)

Recommend two changes to the actuary's selected assumptions across the techniques and justify the changes.

Part b (1.5 points)

For accident year 2014, calculate a revised estimate of ultimate claims for each of the four techniques based on the recommendations made in part a. above.

Part c (1 point)

Assume the actuary selected ultimate claims as the average of the four techniques.

Accident Year Selected Ultimate Claims ($000)
2010 11,250
2011 13,385
2012 15,865
2013 18,483
2014 20,149

Given the revised estimates calculated in part b. above, fully assess the reasonableness of the actuary's accident year 2014 selected ultimate claims estimate of $20,149,000.

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