Brosius

Question 1

Advantage of the least squares method

Answer 1

1. Least squares is more flexible than the link ratio, budgeted loss, and BF methods
2. Least squares is a credibility weighting of the link ratio and the budgeted loss estimates. It gives more (or less) credibility to the loss experience (x) as appropriate
3. Least Squares produces more reasonable results when the data has severe random, year-to-year fluctuations (such as a small book of business or thin data)

Question 2

Advantage of using best linear approximation as a replacement of the Bayesian estimate

Answer 2

1. Simpler to compute
2. Easier to understand and explain
3. Less dependent upon the underlying distribution

Question 3

When is least squares development appropriate?

Answer 3

• The least squares fit does NOT make sense if year to year changes in loss experience are due largely to systematic shifts or distortions in the book of business
• The least squares fit may be appropriate if year to year changes are due largely to random chance

Question 4

Examples on how data can be adjusted before applying the least squares method, in the case of systematic distortions

Answer 4

1. If studying incurred loss data, we can correct for inflation by putting the years on a constant-dollar basis before fitting a line
2. If the business expands, we can divide each year’s losses by an exposure base to eliminate the distortion

Question 5

What can lead to negative a and b values for the least squares method

Answer 5

significant changes in the nature of the loss experience
or sampling error

Question 6

What should you do if a is negative for the least squares method

Answer 6

Our estimate of y would be negative for small values of x. In this case, use the link ratio method

Question 7

What should you do if b is negative for the least squares method

Answer 7

Our estimate of y decreases as x increases. In this case, use the budgeted loss method

Question 8

As we go from more recent AYs to more mature AYs, we should usually see the following patterns (for least squares method)

Answer 8

1. a decreases for more developed years
2. C or LDF decreases for more developed years
3. Z or credibility increases for more developed years (more weight on the link ratio method)