Math 490 Casualty Actuarial Mathematics

1
Math 490 Casualty Actuarial Mathematics

• Fall 2009
• University of Illinois at Urbana-Champaign
• Professor Rick Gorvett
• Session 5 Loss Reserving II
• September 8, 2009

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Agenda

• Review of basic loss development technique and
  essential metrics / quantities
• Other loss reserving methods
• Expected loss ratio
• Bornhuetter-Ferguson
• Diagnostics
• Reserving issues

3
Review of LDF Technique

• General approach of loss development techniques
• Loss development triangle (cumulative data)
• 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.) (ult. loss) (case
  incurred loss)

4
Review of LDF Technique (cont.)

• Possible bases
• Accident Year (AY)
• Policy Year (PY)
• Report Year (RY)
• Possible types of data
• Paid losses (with or without (A)LAE)
• Case incurred losses (with or without (A)LAE)
• Closed claim counts
• Reported / incurred claim counts
• Paid loss severity
• Incurred loss severity

5
Review of LDF Technique (cont.)

• Data relationships
• Cumulative incurred loss cumulative paid loss
  snapshot case reserve
• Cumulative reported / incurred claim count
  cumulative paid claim count snapshot open
  claim count
• Paid severity cumulative paid loss cumulative
  paid claim count
• Reported / incurred severity cumulative
  incurred loss cumulative reported claim count

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Metrics and Quantities of Interest

• Paid loss case reserve (case) incurred loss
• Ultimate AY or PY loss paid loss case reserve
  IBNR
• IBNR (Incurred But Not Reported) loss ultimate
  loss (case) incurred loss
• Total loss reserve ultimate loss paid loss
• Total loss reserve case reserve IBNR
• Loss frequency average severity

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Other Basic Loss Reserving Techniques

• Expected loss ratio (ELR) method
• Loss ratio loss premium
• Ultimate loss premium ELR
• ELR per best estimate (e.g., original loss
  provision in premium per ratemaking process)
• Bornhuetter-Ferguson method
• A middle-ground between the LDF and ELR methods

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Expected Loss Ratio Method
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Bornhuetter-Ferguson (B-F) Method

• Merges the LDF and ELR techniques
• Steps (e.g., for case-incurred B-F)
• (1) Determine the to-ultimate LDF
• (2) Determine the proportion of ultimate loss
  unreported to-date 1 1 / (1)
• (3) Earned premium ELR (a priori) expected
  ultimate loss
• (4) Expected unreported loss (2) (3)
• (5) B-F ultimate loss (4) (case incurred
  loss to- date)

10
Bornhuetter-Ferguson Method
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Bornhuetter-Ferguson Method (cont.)
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Diagnostics

• Relationship of projected ultimate L/R to ELR
• LDF / payout patterns compared with industry or
  other sources
• Internal vs external
• Paid-to-incurred (or to-reserve) ratios
• Closed-to-reported claim count ratios
• Average paid claim
• Reserve as percentage of ultimate loss

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Loss Reserving Issues

• Considering multiple results
• LDF vs ELR vs B-F
• Paid vs incurred vs frequency-severity
• Point estimates vs reserve ranges
• Loss reserve discounting
• Regulatory considerations
• Payment patterns
• Interest rates

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CAS Exam 6, Fall 2005, 10
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CAS Exam 6, Fall 2005, 10 (cont.)
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Next Time

• Loss Reserving III
• Loss reserving principles
• CAS Statement of Loss Reserving Principles
• Accounting issues
• Blanchard study note