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Reserving for Excess of Loss Workers Compensation Contracts

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

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Reserving for Excess of Loss Workers Compensation Contracts

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  1. Reserving for Excess of Loss Workers Compensation Contracts Michael McKnight Chief Actuary, Reinsurance Max Re Ltd. Bermuda

  2. 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

  3. XOL Portfolio(Examples)

  4. 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

  5. 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.

  6. Reporting Patterns

  7. 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”)

  8. “Standard” B-F Approach(for any given Layer) A Priori x (1 - 1/LDFinc) + Incurred Frequency x Average Severity

  9. 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.

  10. “Updated” B-F Approach(for any given Layer) Updated A Priori x (1 - 1/LDFinc) +Incurred Updated Frequency x Average Severity

  11. 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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