Mahler 3 - WC excess ratio

Question 1

Discuss three considerations that would justify truncating of adjusted loss data at a certain $ value (e.g. 100K).

Answer 1

1. maximize reliance on reported data
2. keep enough data points above the truncation point to permit reasonable curve fitting
3. be a round number prior to data thinning out

Question 2

In addition to truncation, shifting, and normalizing, list three adj. that should be made to WC claims before fitting a severity distribution to the data.

Answer 2

1. trend
2. loss development
3. adj. to new benefit level

Question 3

Discuss Mahler’s approach for building a loss distribution model and his rationale for doing so

Answer 3

• Uses empirical data at less than 100K, then he blends exponential and pareto distributions at higher limits after truncating and shifting
• he wanted to rely on actual experience to the extent possible at the lower limits while fitting a curve to make up for sparser data at higher limits.
• The pareto has a thick tail which makes it ideal at very high limits. Exponential works well just above the experience cut off pt.

Question 4

Discuss three advantages of this methodology

Answer 4

1. Actual experience is used for lower layers, where it is credible
2. Fitted ratios are used for higher layers, where experience may not be credible
3. avoids some arbitrary or judgmental division of claims between injury kind

Question 5

Is it reasonable to fit a single curve rather than multiple curves by HG?

Answer 5

reasonable if the shapes of the distributions are similar to diff. RGs after truncation and normalization