Kevin M. Madigan

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CAS Casualty Loss Reserve SeminarSeptember 11,
2001
Reserving for Asbestos Pure IBNR

• Kevin M. Madigan
• MHL/Paratus

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Reserving for Asbestos Pure IBNR

• High Excess (Re)Insurers

• May have significant Asbestos pure IBNR exposure
• Have significant policy data issues
• e.g., old policies/slips not in systems
• Lack valuable qualitative information

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Reserving for Asbestos Pure IBNR

• How to Deal With These Issues?

• Research known asbestos defendants
• Match against policy database
• May take significant effort to build DB
• Use historical experience to project IBNR

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Reserving for Asbestos Pure IBNR

• Using Experience to Project Pure IBNR

• We have developed 2 report year methods inspired
  by

• 1 Cross, Susan L. and Doucette, John P.,
  Measurement of Asbestos Bodily Injury
  Liabilities, PCAS, Vol LXXXIV, Nos. 160 and 161,
  pgs 187 -300
• 2 Haidu, Jim, Estimating a Reinsurers
  Liabilities for Asbestos and Environmental
  Losses, 1996 CAS CLRS

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Reserving for Asbestos Pure IBNR

• Using Experience to Project Pure IBNR

• Both methods use (report year) actual or modeled
  losses to arrive at a factor that is applied to
  exposed policy limits

• We are implicitly assuming the existence of
  modeled losses at the account or policy level
• We are modeling GROSS losses

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Reserving for Asbestos Pure IBNR

• Using Experience to Project Pure IBNR

• Method 1 uses account experience

• Method 2 uses policy experience
• Should any of the historical experience be
  excluded?

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Reserving for Asbestos Pure IBNR

• Method I

• Pricing Approach

• Allocate experience to layers
• Calculate burn rates
• Apply to potential IBNR policies

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Reserving for Asbestos Pure IBNR

• Method I

• Allocate experience to layers

• Each account has an actual (closed accounts) or
  modeled (open accounts) annual loss distribution

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Reserving for Asbestos Pure IBNR

• Method I

• Calculation of Burn Rates

• Example for Report Year 19XX

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Reserving for Asbestos Pure IBNR

• Method I

• Calculation of Burn Rates

• Ideally want burn rate confidence intervals, from
  which baseline confidence intervals can be
  selected for each layer

Burn Rate Confidence Intervals
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Reserving for Asbestos Pure IBNR

• Method I

• Apply Burn Rates to potential IBNR policies

• Requires assumptions regarding
• Reporting Pattern(s)
• Trend Assumptions
• e.g., 2 annual decay in burn rate
• Exposed Policy Limits

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Reserving for Asbestos Pure IBNR

• Method I

Lower limit of C.I. of Burn Rate for Layer
26
Exposure in Layer
500,000,000

• Apply
• Burn
• Rates

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Reserving for Asbestos Pure IBNR

• Comparison of Methods

• Method I computes an annual rate for each
  layer, and charges the exposed policies the
  corresponding price.
• Method II computes one factor to be applied to
  the limits of each policy

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Reserving for Asbestos Pure IBNR

• But wait!

• We have a wide assortment of attachment points
  and policy limits, so it hardly seems right to
  apply the same factor to each policy.
• Does a 25M x 200M policy have the same exposure
  to loss as a 4M x 1M policy?
• Of course not!

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Reserving for Asbestos Pure IBNR

• Method II

Exposed policy limits are adjusted
as follows
Adjusted exposure TPE Pr( GUL gt AP)
where TPE Total Policy Exposure GUL Ground-
Up Loss AP Policy Attachment Point
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Reserving for Asbestos Pure IBNR

• Method II

• Calculate historical ratios of loss to adjusted
  exposure for each report year (lets call them
  loss cost factors)

• Select a base line confidence interval for the
  loss cost factors
• Make assumptions regarding reporting pattern(s)
  and cost trend(s)

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Reserving for Asbestos Pure IBNR

• Method II

• Calculate ratios of loss to adjusted exposure

• Example RY 19xx

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Reserving for Asbestos Pure IBNR
0.834
Baseline Loss Cost Factor
Method II

• Select a base
• line for the
• loss cost factors

0.860
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Reserving for Asbestos Pure IBNR
Method II

• Make assumptions regarding reporting pattern(s)
  and cost trend(s)

Trended Projected Loss Cost Factor
0.717
Potential Policies
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Reserving for Asbestos Pure IBNR

• Other Issues

• Loss trend may be (probably is?) positive, or
  trend rate may not be constant
• Policy buy backs
• Distinguish products liability from other
  liability
• Not only source of pure IBNR
• Commutation strategy
• Reinsurance collections/collectibility