Actuarial Notes

CAS Exam 7 Spring 2014, Question 4

Study guide: Exam 7

Given the following loss information:

Year Cumulative Reported Losses ($000) at 12 Months 24 Months 36 Months 48 Months 60 Months 72 Months
2008 200 1,000 1,500 1,800 2,100 2,100
2009 400 800 1,000 1,500 1,800
2010 800 1,500 2,000 2,200
2011 1,200 2,000 2,200
2012 400 1,800
2013 200
DF (t-statistic for 0.90 at Various Degrees of Freedom) 1 2 3 4 5 6 7
t-statistic 3.08 1.89 1.64 1.53 1.48 1.44 1.42
  • Assume T = r\left[(n-2)/(1-r^2)\right]^{1/2} is t-distributed with n-2 degrees of freedom where r is the sample correlation coefficient.

Part a (3.25 points)

Evaluate whether the triangle above meets the assumption that the age-to-age factors are independent from 12 months to 36 months, using a 10% t-statistic significance standard.

Part b (0.5 points)

State two other basic chain-ladder assumptions needed for least squares optimality.

Answer this question and see the worked solution

Concepts tested

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