Math 490 Casualty Actuarial Mathematics

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Math 490 Casualty Actuarial Mathematics

• Fall 2009
• University of Illinois at Urbana-Champaign
• Professor Rick Gorvett
• Session 4 Loss Reserving I
• September 3, 2009

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Agenda

• Purpose of Loss Reserving
• Loss data
• Types of reserves
• Key dates
• Types of data
• Reserving issues
• The basic loss development technique

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Purpose of Loss Reserving

• Determine the amount of outstanding loss
  liabilities, as of a certain date, associated
  with claims incurred by the insurance company on
  or prior to that date
• Claims incurred on earned premium
• Balance sheet impact
• Biggest liability item for insurance companies
• Larger reserve ? smaller surplus (equity)
• Income statement impact

4
Loss Data

• Types of loss data
• Paid losses
• Incurred losses
• Allocated loss adjustment expenses (ALAE)
• Other expenses
• Basis of loss data
• Accident year
• Policy year
• Calendar year
• Report year

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Types of Reserves

• Provisions for claim obligations associated with
• Case reserves
• Future development on known claims
• Re-opened claims
• Incurred but not reported (IBNR)
• Reported but not yet recorded

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Key Dates in the Life of a Claim

• Accident date
• Report date
• Activity dates
• Reserve set up or changed
• Payments made
• Closed date
• Re-opened date (occasionally)

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Types of Data for Loss Reserving

• Type of data used can vary with the reserving
  technique
• Loss development triangles are the traditional
  context within which loss reserves are estimated
  and analyzed
• General description of process
• Accident / policy year losses at sequential
  valuation dates
• Age to age factors (link ratios)
• To-ultimate loss development factors

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Types of Data (cont.)

• Types of loss data analyzed
• Case incurred losses (and possibly ALAE or even
  LAE)
• Paid losses
• For both cumulative versus incremental
• Claim counts
• Paid versus reported
• Cumulative versus incremental
• Average claim size (severities)
• Paid versus incurred
• Open versus closed claims

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Reserving Issues

• Availability of data
• Volume of data
• How to treat large losses
• Other data anomalies including possible errors!
• Line of business
• Claim handling procedures
• Reserving philosophies
• Payment philosophies
• Underwriting considerations
• Legal / judicial climate

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The Basic Loss Development Technique

• Loss development method
• Accident year
• Report year
• Policy year
• Note loss development techniques can be
  performed on any or all of the following (and
  more) bases
• Paid losses
• Case incurred losses
• Frequency (claim counts) and severity (average
  claim size)

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Paid Loss Development Triangle
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Age-to-Age Development Factors(Link Ratios)
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Projection of Ultimate Losses and Loss Reserves
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General Loss Development Approach

• Loss development triangle
• Age-to-age factors (link ratios)
• Approaches to selecting factors e.g.,
• Straight average
• Average of last three years
• (Middle) 3 of 5 years
• Weighted average (by dollars)
• To-ultimate loss development factors
• For each (accident) year (actual loss) (LDF)
  estimated ultimate loss
• Reserve (ultimate loss) (to-date paid loss)
• IBNR (broad defn.) (ultimate loss) (case
  incurred loss)

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CAS Exam 6, Fall 2007, 7
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CAS Exam 6, Fall 2008, 9a
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CAS Exam 6, Spring 2004, 2
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Next Time

• Loss Reserving II
• Other techniques
• Chapter 5 of Foundations of Casualty Actuarial
  Science