INTRODUCTION TO REINSURANCE EXPERIENCE AND EXPOSURE by vbm17056

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									INTRODUCTION TO REINSURANCE
EXPERIENCE AND EXPOSURE RATING

 SUMMARY AND RECONCILIATION OF ESTIMATES


 MICHAEL E. ANGELINA - TOWERS PERRIN
 CAS RATEMAKING SEMINAR
 MARCH 11, 2004
 PHILADELPHIA, PA
KEY ASSUMPTIONS

You are the underwriter/actuary of the assumed
 reinsurance division, what should you be thinking
 about:
   Hazard group selection
   Loss ratios
   Expense loadings
   Claim frequencies
   Tail factors
   Layer severities
   Credibility of experience
   Results of u/w audit

                                                     2
Reconciliation of Estimates

Goal - determination of a final estimate

                               Expected   Ultimate      Excess
 Recap of results              Counts     Loss & ALAE   Severity

     Exposure Estimate            2.3        82.1        28.0
     Classical Burning Cost       1.09       68.4        15.9
     Freq/Severity-Industry       0.85       69.5        12.3
     Experience Estimate          0.96       67.7        14.2

Wide range of results between experience and exposure
   Severity relatively flat
   Variation in expected counts/losses

                                                                   3
     Experience Rating - Frequency Based Method
     Projected # of Claims for Rating Year

      (1)           (2)          (3)        (4)        (5)         (6)           (7)
                             Actual #>                Claim
                 Detrended   Detrended   Frequency    Count    Adjustment     Projected
  Accident         Data        Data        Trend      Dev't     for Growth   # of Claims
   Year            Limit       Limit       @ 2%      Factors   in Premium    >Data Limit
                   6.0%                                                       [3x4x5x6]

    1999            74,726         4.0       1.104     1.125         2.960             14.7
    2000            79,209         7.0       1.082     1.238         2.162             20.3
    2001            83,962         2.0       1.061     1.671         1.684              6.0
    2002            89,000         9.0       1.040     2.506         1.509             35.4
    2003            94,340         2.0       1.020     6.265         1.270             16.2

 Total All yrs                    24.0                                                 92.6
 Total 99-02                      22.0                                                 76.3

Rate Year 2004     100,000                                                         20.00




                                                                                           4
                  RECAP OF ESTIMATES
                  Ultimate Losses

                 4,000


                 3,000
Dollars (000s)




                 2,000


                 1,000


                    0
                             1999     2000         2001         2002         2003       Burning
                                                                                         Cost
                         Reported   Indicated Ultimate Losses     Exposure          Experience




                                                                                                  5
                      RECAP OF ESTIMATES
                      Expected Counts > $100k

                 40

                 35
                 30
Dollars (000s)




                 25

                 20

                 15

                 10

                 5

                 0
                         1999     2000          2001         2002         2003        Burning
                                                                                       Cost
                      Reported   Indicated Ultimate Losses     Exposure          Experience




                                                                                                6
Reconciliation of Estimates

 Which method yields best estimate?
   Experience estimates
     Test at lower layers
       Results for frequency/severity and burning cost should be consistent
     Considerations
       credibility of data - 40 XS claims?
       loss development factors - reflecting claim audit?
       load for ALAE (explicit/implicit?)
       adjust for claim impact of premium growth - deterioration in U/W?
       account for change in policy limits?




                                                                               7
Reconciliation of Estimates

  Which method yields best estimate (con’t)
    Exposure estimates
      Allocation of premium consistent with company’s
      Historical comparison of XS premium to losses
        suggest different loss ratio for layer?
      Considerations
        appropriateness of size of loss curve
           test with claim emergence at different attachment points
           calculate implied claim counts to company experience
           compare industry curve to company fitted curve
           fitting curve is not trivial (development on individual claims)
        adequacy of loss ratio
           reflect claim audit findings
           adjust for implication on growing business
           account for differences in excess layer vs. primary layer




                                                                              8
                Reconciliation of Estimates
Limited Average Severity


                           1.3

                           1.2

                           1.1

                           1.0

                           0.9

                           0.8




                                                                                           0

                                                                                                  0

                                                                                                         0
                               0

                                     0

                                           0

                                                 0

                                                       0

                                                             0

                                                                   0

                                                                         0

                                                                               0

                                                                                     0
                             10

                                   15

                                         20

                                               25

                                                     30

                                                           35

                                                                 40

                                                                       45

                                                                             50

                                                                                   75

                                                                                           00

                                                                                                  50

                                                                                                         00
                                                                                         1,

                                                                                                1,

                                                                                                       2,
                                                              Policy Limit
                                                           Ind-M L     Ind-M       Act



                                                                                                              9
                        Reconciliation of Estimates

                        60
Expected Claim Counts




                        50

                        40

                        30

                        20

                        10

                         0
                              50     75     100        150       200     > 250
                                                  Attachment Point

                               Exposure    F/ S - Industry     F/ S - Company    Actual



                                                                                          10
Audience Underwriting

                                  Recap of Results

                        Ultimate         Exp Counts           ALAE     Implied
                     Loss & ALAE             >100k             Load    XS L/R


Exposure                   2.30               28.0             21%     62.1%
Burning Cost               1.09               15.9             8.5%    31.8%
Frequency/Severity         0.85               12.3             7.5%    24.6%
  (Industry)
Experience                 1.00               14.0             8.0%    29.1%


* assumes premium allocated to layer is 3,717 (from exposure method)

                                                                                 11
Reconciliation of Estimates

 Goal - Sensitivity test indications
 Experience Indications (burning cost)
   Selected                   1,000       2.5%
   Alter Selection            1,200       BF: 2 recent yrs
   ALAE Differences             111       18% vs 8%
   Revised Selection          1,311       3.3%
 Experience Indications (frequency / severity)
   Selected                    851         2.4%
   Alter Selection            1,080        Different weights
   ALAE Differences             105        18% vs 7.5%
   Revised Selection          1,185        3.0%
 Final Selection                1,250     3.1%


                                                                12
Reconciliation of Estimates
   Goal - Move expected ultimates to similar base
   Exposure Indications
     Selected           2,304          5.8%
     Alter Selection    1,593          higher % Table 1
     ALAE Differences     (40)         18% vs 21%
     Revised Selection  1,553          3.9%
   Experience Indications (Selected)
     Revised Selection    1,250        3.1%
       implied loss ratio for layer    34.4%
   Final Selection            1,450    3.625%
     implied loss ratio for layer      39%




                                                           13
Reconciliation of Estimates Scenario Testing

 Move away from point estimate of methods and look at a range of
  possible outcomes
   Exposure
    size of loss table/loss ratio
    what assumptions would get result to experience rate
      20% loss ratio, lower hazard curve, less ALAE loading, combination
        of all three
  Experience
    LDF’s, claim counts, size of loss curve (industry or company)
    what assumptions get result to exposure rate
      54 claims above 50k, heavier tail factor (1.238 @ 60 months to 2.2)
 Assign weights to various outcomes and determine a new
  expected loss estimate
  Credibility

                                                                             14
Reconciliation of Estimates

     Leads to stochastic applications
       Need to assign probabilities to various assumptions/scenarios
       Think about independence of variable
       Address parameter/process risk
     Results in better pricing for AAD considerations, swing plans, stop
      loss treaties, etc.




                                                                        15

								
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