|
Line of Business |
Commercial Auto |
|
Policy Limits |
8,000,000 |
|
Attachment Point |
2,000,000 |
|
Trend Applied to Limit & Attachment |
0.00% |
|
Number of Years |
10 |
|
Claims x Year |
100; 100; 100; 100; 100; 100; 100; 100; 100; 100 |
|
Observed Trend |
2.00% |
|
Tolerance |
0.25% |
|
|
| =Σ[(1) x (2)] |
Average Prior |
5.00% |
| (1) |
A Priori Trends |
0.00% |
1.00% |
2.00% |
3.00% |
4.00% |
5.00% |
6.00% |
7.00% |
8.00% |
9.00% |
10.00% |
| (2) |
Prior Trend Weight |
2.50% |
5.00% |
7.50% |
12.50% |
15.00% |
15.00% |
15.00% |
12.50% |
7.50% |
5.00% |
2.50% |
| (3) |
Likelihood of Observation |
3.52% |
3.32% |
3.88% |
3.70% |
4.38% |
3.88% |
4.10% |
4.22% |
4.06% |
3.86% |
3.62% |
| (4) = (2) x (3) |
Joint Probability |
0.09% |
0.17% |
0.29% |
0.46% |
0.66% |
0.58% |
0.62% |
0.53% |
0.30% |
0.19% |
0.09% |
| (5) = (4) / Σ(4) |
Posterior Trend Weight |
2.21% |
4.17% |
7.32% |
11.63% |
16.52% |
14.63% |
15.46% |
13.26% |
7.66% |
4.85% |
2.28% |
|
|
|
Average Simulated Trend |
-0.01% |
-0.01% |
0.03% |
0.03% |
0.05% |
0.03% |
0.04% |
0.02% |
-0.01% |
0.00% |
-0.03% |
|
2.5th Percentile |
-2.30% |
-2.19% |
-2.15% |
-2.14% |
-2.14% |
-2.27% |
-2.11% |
-2.19% |
-2.21% |
-2.23% |
-2.26% |
|
97.5th Percentile |
2.28% |
2.19% |
2.24% |
2.24% |
2.32% |
2.22% |
2.27% |
2.21% |
2.20% |
2.23% |
2.22% |
|
|
| (6) = Σ[(1) x (5)] |
Credibility-Weighted Trend Estimate |
5.06% |
|
|
|
|
* As above using alternate trend on Limit |
|
|
* Trend applied to limit & attachment |
4.00% |
|
|
|
|
Average Prior |
5.00% |
|
A Priori Trends |
0.00% |
1.00% |
2.00% |
3.00% |
4.00% |
5.00% |
6.00% |
7.00% |
8.00% |
9.00% |
10.00% |
|
Prior Trend Weight |
2.50% |
5.00% |
7.50% |
12.50% |
15.00% |
15.00% |
15.00% |
12.50% |
7.50% |
5.00% |
2.50% |
|
Likelihood of Observation |
3.74% |
3.70% |
3.86% |
3.74% |
4.08% |
3.46% |
4.12% |
3.32% |
3.80% |
4.04% |
3.72% |
|
Joint Probability |
0.09% |
0.19% |
0.29% |
0.47% |
0.61% |
0.52% |
0.62% |
0.42% |
0.29% |
0.20% |
0.09% |
|
Posterior Trend Weight |
2.47% |
4.89% |
7.66% |
12.37% |
16.19% |
13.73% |
16.35% |
10.98% |
7.54% |
5.34% |
2.46% |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Average Simulated Trend |
4.07% |
4.07% |
4.03% |
4.03% |
4.01% |
4.00% |
4.02% |
4.03% |
4.06% |
4.07% |
4.05% |
|
2.5th Percentile |
1.84% |
1.81% |
1.78% |
1.83% |
1.76% |
1.74% |
1.75% |
1.69% |
1.73% |
1.81% |
1.83% |
|
97.5th Percentile |
6.33% |
6.41% |
6.37% |
6.30% |
6.33% |
6.31% |
6.41% |
6.26% |
6.31% |
6.43% |
6.37% |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Credibility-Weighted Trend Estimate |
4.99% |
|
|
|
|
|
|
|
|
|
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