Actuarial Notes

CAS Exam 5 Spring 2016, Question 22

Study guide: Exam 5

Given the following information:

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

Accident Year 12 24 36 48 60
2011 10,000 20,000 25,000 27,000 27,000
2012 10,000 20,000 25,000 27,000
2013 10,000 20,000 25,000
2014 10,000 20,000
2015 10,000

Cumulative Paid ALAE ($) as of (months):

Accident Year 12 24 36 48 60
2011 500 1,500 2,250 2,700 2,700
2012 500 1,500 2,250 2,475
2013 500 1,500 1,875
2014 500 1,000
2015 250

Paid Claims Development Factors:

Accident Year 12-24 24-36 36-48 48-60
2011 2.00 1.25 1.08 1.00
2012 2.00 1.25 1.08
2013 2.00 1.25
2014 2.00

Paid ALAE Development Factors:

Accident Year 12-24 24-36 36-48 48-60
2011 3.00 1.50 1.20 1.00
2012 3.00 1.50 1.10
2013 3.00 1.25
2014 2.00
Calendar Year Earned Premium ($) Paid Claims ($) Paid ALAE ($) Paid ULAE ($)
2011 50,000 27,000 2,700 3,240
2012 50,000 27,000 2,700 3,240
2013 50,000 27,000 2,700 3,240
2014 50,000 27,000 2,700 3,240
2015 50,000 27,000 1,350 4,212
  • Prior to 2015, the insurer operated in a steady state environment. Data prior to accident year 2011 exists but is not shown above.
  • Claims and ALAE trend = 0%.
  • Total case outstanding as of December 31, 2015 = $21,000.
  • Total IBNR as of December 31, 2015 = $5,000.
  • In 2015, the insurer began to use its own legal department on more claims in an effort to reduce legal expenses.
  • Legal department salaries are not allocated to specific claims and thus are recorded as ULAE.
  • The legal fees from outside attorneys are billed to specific claims and recorded as ALAE.
  • The change in attorney expenses resulted in a 50% decline in ALAE and a 30% increase in ULAE; the new expense ratios are expected to persist through future calendar years.

Part a (1 point)

Estimate the total unpaid ALAE as of December 31, 2015 for all accident years.

Part b (0.5 points)

Estimate the total unpaid ULAE as of December 31, 2015 using the classical technique.

Part c (0.75 points)

Assume that prior to the change in 2015, half of ULAE was sustained when claims were reported. Fully assess the reasonableness of the estimate provided in part b. above.

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