Reserving for Excess of Loss Workers Compensation Contracts by vow15418

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									 Reserving for Excess of Loss
Workers Compensation Contracts


Michael McKnight
Chief Actuary, Reinsurance
Max Re Ltd.
Bermuda
          XOL WC Portfolio
• Focus on typically smaller regional carriers
  and state funds
• Often multiple stacked layers; for example:
  – $500k xs $500k and $4m xs $1m
  – $750k xs $250k, $1m xs $1m and $3m xs $2m
  – $1m xs $1m, $3m xs $2m and $5m xs $5m
            XOL Portfolio
                         (Examples)
6,000,000




5,000,000




4,000,000


                                                      3rd Layer
                                                      2nd Layer
3,000,000
                                                      1st Layer
                                                      Retained


2,000,000




1,000,000




       0
            Contract 1      Contract 2   Contract 3
         XOL WC Portfolio
                 (Continued)

• Participation percentages vary from 10% to
  100%
• Contracts typically have limited
  reinstatements
• Some contracts have premiums paid on
  reinstatements
• Some contracts have annual aggregate
  deductibles
                  Problem
• Excess Workers Compensation is a slow
  developing line of business. How can we
  get a faster indication of the results?
                  Solution
• An approach based on
  – The fact that claims in a lower layer are
    reported faster than claims in higher layers.
  – The contractual reporting requirements of
    Excess of Loss contracts.
         Reporting Patterns
              Percentage of Claims Reported

100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%                                              XS $250,000
30.0%                                              XS $500,000
20.0%                                              XS $1,000,000

10.0%
 0.0%
         36     48             60             72             84
                        Months of Maturity
       Contractual Claim Reporting
•   Fatality;
•   Amputation;
•   Spinal cord damage;
•   Brain damage;
•   Blindness;
•   Extensive burns;
•   Multiple fractures; OR
• A claim is reserved for more than 50.0% of
  the attachment (“Monitoring Threshold”)
  “Standard” B-F Approach
            (for any given Layer)



A Priori x (1 - 1/LDFinc) + Incurred



  Frequency x Average Severity
    Updating the Layer Frequency
Monitoring Threshold Frequency

A Priori Freq x (1 - 1/LDFrept) + Number Reported


Layer Frequency

Monitoring Threshold Frequency x [1 - F(Layer Attachment)]

Where F(x) is the cumulative size of loss distribution with a base equal to the Monitoring
Threshold.
    “Updated” B-F Approach
               (for any given Layer)




Updated A Priori x (1 - 1/LDFinc) +Incurred



 Updated Frequency x Average Severity
               Pros / Cons
• Pros
  – Intuitive – focus on number of claims
  – Quicker look at results
  – Ties upper and lower layers together
• Cons
  – Inputs – Size of loss distributions, reported
    claim patterns by layer, frequency
    assumptions
  – Possibly too fast – could be too responsive to
    number of reported claims

								
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