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Loss Reserving

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Estimated Loss Reserve = Total Expected Losses x % of Losses to Be Paid in Future ... but includes case loss reserves. Additional Reserving Requirements ... – PowerPoint PPT presentation

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Title: Loss Reserving


1
Loss Reserving
  • Anatomy of a claim
  • 12/15/99 Auto accident
  • 12/20/99 Insured reports
  • accident to agent
  • 1/7/00 Claim recorded
  • 2/3/00 10,000 reserve set
  • 1/8/01 Pay 3000 medical expenses
    offer 15,000 settlement
  • 15,000 reserve set
  • 7/2/01 Offer refused
  • 9/8/01 Lawsuit files
  • 4/1/02 20,000 reserve
  • 1/6/03 40,000 reserve
  • 10/6/04 Court awards 32,000
  • Incurred loss development
  • Accident Year 1999
  • 1999 IBNR
  • 2000 10,000
  • 2001 18,000
  • 2002 23,000
  • 43,000
  • 2004 32,000

2
Definitions
  • Individual claim file estimates
  • Paid loss development
  • Considers only loss payments
  • Paid loss development factors
  • Incurred loss development
  • Paid plus case reserves
  • Incurred loss development factors
  • Loss adjustment expenses
  • Allocated
  • Unallocated

3
Loss reserve methods
  • Unsophisticated methods
  • Case reserve plus
  • Expected loss ratio method
  • More accurate methods
  • Chain ladder or loss development triangle method
  • Bornhuetter-Ferguson method
  • Frequency and severity estimates

4
Cumulative Loss Payments
  • Accident Development Age (Months)
  • Year 12 24 36 48 60 72 84 96
  • 1992 5445 8602 11052 12464 13064 13416 13847 140
    32
  • 1993 5847 9333 10699 11547 12592 13646 14015
  • 1994 5981 10835 12783 15337 17017 17506
  • 1995 7835 12288 16176 19511 21599
  • 1996 9763 16280 19843 23827
  • 1997 10745 16929 21478
  • 1998 14137 22253
  • 1999 15162
  • Assume that no further losses are paid after 96
    months.

5
Paid Loss Development Factors
  • Accident Link Factors
  • Year 12-24 24-36 36-48 48-60 60-72 72-84 84-96
  • 1992 1.580 1.285 1.128 1.048 1.027 1.032 1.013
  • 1993 1.596 1.146 1.079 1.090 1.084 1.027
  • 1994 1.812 1.180 1.200 1.110 1.029
  • 1995 1.568 1.316 1.206 1.107
  • 1996 1.668 1.219 1.201
  • 1997 1.576 1.269
  • 1998 1.574
  • Ave. 1.625 1.236 1.163 1.089 1.047 1.030 1.013
  • Age- 2.779 1.710 1.384 1.190 1.092 1.043 1.013
  • Ultimate

6
Estimated Loss Reserves Based on Average Paid
Loss Development Factors
  • Age to
  • Accident Paid to Ultimate Ultimate Loss
  • Year Date Factor Losses Reserve
  • 1992 14032 1.000 14032 0
  • 1993 14015 1.013 14197 182
  • 1994 17506 1.043 18259 753
  • 1995 21599 1.092 23586 1987
  • 1996 23827 1.190 28354 4527
  • 1997 21478 1.384 29726 8248
  • 1998 22253 1.710 38053 15800
  • 1999 15162 2.779 42135 26973
  • Total 149872 208342 58470

7
Expected Loss Ratio Method
  • Estimated Ultimate Losses Expected Loss Ratio x
    Earned Premium
  • Estimated Loss Reserve Estimated Ultimate
    Losses - Losses Paid to Date
  • Example
  • 1999 Earned Premium 65,000
  • Expected Loss Ratio 60
  • Estimated Ultimate Losses 39,000
  • Losses Paid to Date 15,162
  • Estimated Loss Reserve 23,838

8
Bornhuetter-Ferguson Method1999 Accident Year
  • Estimated Loss Reserve Total Expected Losses x
    of Losses to Be Paid in Future
  • of Losses to Be Paid in Future
  • 1-(1/Age-Ultimate Factor)
  • Example 12 Month-Ultimate 2.779
  • of Losses Paid After 12 Months 1-1/2.779.640
  • Total Expected Losses 65,000 x .6039,000
  • Estimated Loss Reserve 39,000 x .640 24,960

9
Results of Different Loss Reserve Methods
Accident Year 1999
  • Paid Loss Development 26,973
  • Expected Loss Ratio 23,838
  • Bornhuetter-Ferguson 24,960

10
Frequency and Severity Estimates
  • Calculate Incurred Claim Counts
  • Determine Loss Frequency Claims/Exposure
  • Determine Average Payment per Claim or
  • Average Incurred Loss per Claim (Severity)
  • Trend Frequency and Severity Separately
  • Combine to Determine Ultimate Incurred Losses

11
Incurred Loss Development
  • Similar to paid loss development, but includes
    case loss reserves

12
Additional Reserving Requirements
  • Loss Adjustment Expense
  • Allocated
  • Sometimes included with losses
  • Unallocated
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