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Introduction to Reinsurance Exposure Rating

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1. Introduction to Reinsurance. Exposure Rating. CAS Ratemaking Seminar. Session REI-47 ... ikaplan_at_gcr.com. 2. Exposure Rating Objectives: Estimate Expected ... – PowerPoint PPT presentation

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Title: Introduction to Reinsurance Exposure Rating


1
Introduction to Reinsurance Exposure Rating
CAS Ratemaking Seminar Session REI-47 March 12,
2001 - Las Vegas
Ira Kaplan ikaplan_at_gcr.com
2
Exposure Rating Objectives Estimate Expected
Excess Losses
  • Analyze the premium profile
  • Estimate the expected loss ratio
  • Estimate the layering of the expected losses

2
3
Treaty Submission Information Needed
  • Premiums by policy limits
  • What business exposes the layer to loss?
  • Premiums by G.L. class code
  • How does the business expose the layer to loss?
  • Historic loss ratios
  • This takes us from premiums to losses

3
4
Exposure Rating Assumptions Policy Limits
Profiles
  • Premium Distribution by Policy Limit
  • Limit Est. 01 Premium of Total
  • 100/100 7,000,000 17.5
  • 300/300 8,520,000 21.3
  • 500/500 10,000,000 25.0
  • 1000/1000 14,480,000 36.2
  • 40,000,000

4
5
Exposure Rating Assumptions GL class profiles
  • 100 Premises/Operations
  • 100 Table 2

5
6
Distribution of Premium to Layer
  • Premium Distribution by Policy Limit
  • Limit Premium Retention 100 Xs100 Xs 200
  • 100/100 7,000 7,000 0 0
  • 300/300 8,520 6,842 1,066 612
  • 500/500 10,000 7,379 1,150 1,471
  • 1000/1000 14,480 9,641 1,502 3,336
  • 40,000 30,862 3,717 5,420
  • NOTE All values in thousands

6
7
The distribution of losses to layer is not the
same as the distribution of premiums to layer
  • - alae
  • - risk load

7
8
Distribution of Premium and Expected Loss to
Layer Policy Limit 500/500
  • Premium Loss
  • Layer Distribution Distribution
  • 0-100 73.8 67.8
  • 100-200 11.5 14.7
  • Above 200 14.7 17.5

8
9
Selection of Direct ELR
  • Review historic experience
  • Test reserve adequacy
  • Understand business plan changes
  • Review rate level changes
  • Selection 40 (excl. alae)

9
10
Allocation of Premium Loss to Layer
  • Limit Retention 100 Xs100 Xs200 Total
  • 100/100 Premium 7,000 0 0 7,000
  • Loss 2,800 0 0 2,800
  • 300/300 Premium 6,842 1,065 612 8,520
  • Loss 2,551 552 304 3,408
  • 500/500 Premium 7,379 1,150 1,472 10,000
  • Loss 2,714 588 698 4,000
  • 1000/1000 Premium 9,641 1,502 3,336 14,480
  • Loss 3,537 766 1,485 5,792
  • Total Premium 30,862 3,717 5,421 40,000
  • Loss 11,602 1,907 2,490 16,000

10
11
ALAE and combination losses need to be included
11
12
ALAE by Layer
  • Retention 100 Xs100 Xs200 Total
  • Premium 30,862 3,717 5,421 40,000
  • ExpLoss 11,603 1,907 2,490 16,000
  • ALAE 42.9 20.9 18.6 36.6
  • ALAE 4,988 398 465 5,851
  • LossALAE 16,591 2,304 2,956 21,851
  • LLAE Ratio 53.8 62.0 54.5 54.6

12
13
Loss Ratios by Layer
13
14
Expected Frequency Severity for 100,000 Layer
  • Expected Loss 1,906,650
  • Expected Avg Severity 68,207
  • Expected of Claims 27.95

14
15
How to Test the Exposure Rating Indications
  • Review the premium profile selections
  • Review the selected ELR
  • Consider the appropriateness of the ISO loss
    curves
  • Look at actual loss information
  • Experience Rating

15
16
Pro Rata ALAE
  • Loss ALAE L ALAE
  • Total 640 320 960
  • 600 x 400 240 120 360
  • Ceded Loss x Direct Expenses Ceded Loss
  • Direct Loss
  • Ceded Loss x (Direct Expense Direct Loss)
  • Direct Loss
  • Ceded Loss x ( 1 Direct Expense )
  • Direct
    Loss

16
17
ALAE Treatment - case 1
18
ALAE Treatment - case 2
19
ALAE Load Can Vary
  • By layer - as seen earlier
  • Model with two way variability
  • Load decreases by limit
  • ALAE is then allocated to layers
  • One allocation formula for Pro Rata
  • A more complicated one for Added To

20
Introduction to Reinsurance Exposure Rating?
NOT!
  • Intro to Excess of Loss Reinsurance Exposure
    Rating approach to estimating LossALAE for GL
  • Basics of Reinsurance Pricing by David R.
    Clark, Exam 6 Study Note

21
Basics of Reinsurance Pricing
  • Proportional Treaties
  • Property Per Risk XS
  • Casualty Per Occurrence XS
  • WC, Umbrella, AADs
  • Aggregate Distributions
  • Property Cat
  • Final Price -
  • risk loads, expenses, etc.
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