chap4 by wpr1947

VIEWS: 2 PAGES: 36

									    P/C RATEMAKING
    AND LOSS
    RESERVING
    by Robert Brown and Leon
    Gottlieb


  CHAPTER 4: LOSS RESERVING

 The financial condition of an insurance
company can not be adequately assessed
  without sound loss reserve estimates.
                         -- CAS Chapter 5
                                                                      2




     I. Introduction
1.    Ratemaking and Loss Reserving are two most
      important P&C actuarial jobs
2.    Qualified actuary must attest to adequacy of year-end
      reserves (by law)
     a.   to protect policyholders
     b.   to allow distribution of reported profits
     c.   to indicate level of solvency to potential investors (may
          be conservative)
     d.   to provide ultimate claims estimates to pricing actuary
                                                        3


II. How Outstanding Claims
Payments Arise
1. There can be several delays in the claims-payment
   process
   a. between accident incurral and reporting
   b. between reporting and recording in head
       office
   c. between claim file opened and final dollar
       paid (i.e., growth or decline on known claims)
2. Large claims tend to settle last
3. Try to model future claim payment patterns based
   on past patterns
                                                  4




          A Hypothetical Claim



             10/15
             Claim
             Event


          2003        2004   2005   2006   2007
Loss
Reserve
Carried          $0
12/31
                                                          5




          A Hypothetical Claim
                        12/20/04
                          Claim
                       Reported to
                       Agent, but
                         Not Yet
             10/15
                        Recorded
             Claim
                        by Insurer
             Event


          2003        2004           2005   2006   2007
Loss
Reserve
Carried          $0          $0
12/31
                                                                6




          A Hypothetical Claim
                                      09/09/05
                        12/20/04
                                     Pay $3,000
                          Claim
                                      Medical
                       Reported to
                                     Expenses;
                       Agent, but
                                        Offer
                         Not Yet
             10/15           01/07/05 $15,000
                        Recorded
             Claim            Claim Settlement
                        by Insurer
             Event          Recorded


          2003        2004          2005          2006   2007
Loss
Reserve
Carried          $0          $0         $20,000
12/31
                                                                          7




          A Hypothetical Claim
                                      09/09/05
                        12/20/04
                                     Pay $3,000
                          Claim
                                      Medical
                       Reported to
                                     Expenses;
                       Agent, but
                                        Offer
                         Not Yet
             10/15                          02/02/06
                             01/07/05 $15,000
                        Recorded
             Claim                       Offer Refused;
                              Claim Settlement
                        by Insurer
             Event          Recorded       Go to Court


          2003        2004          2005          2006             2007
Loss
Reserve
Carried          $0          $0         $20,000          $40,000
12/31
                                                                               8




          A Hypothetical Claim
                                      09/09/05
                        12/20/04
                                     Pay $3,000
                          Claim
                                      Medical
                       Reported to
                                     Expenses;
                       Agent, but
                                        Offer
                         Not Yet
             10/15                          02/02/06
                             01/07/05 $15,000                   10/06/07
                        Recorded
             Claim                       Offer Refused;
                              Claim Settlement                Court Decision;
                        by Insurer
             Event          Recorded       Go to Court         Pay $32,000


          2003        2004          2005          2006             2007
Loss
Reserve
Carried          $0          $0         $20,000          $40,000          $0
12/31
                                                                                 9




          A Hypothetical Claim
                         12/20/04          09/09/06
                      Claim Reported      Pay $3,000
                       to Agent, but Medical Expenses;
                       Not Recorded      Offer $15,000
                         by Insurer       Settlement
           10/15/96             01/07/05       02/02/06           10/06/07
            Claim                Claim      Offer Refused;      Court Decision;
            Event              Recorded      Go to Court         Pay $32,000


          2003        2004           2005           2006             2007
Loss
Reserve
Carried          $0           $0          $20,000          $40,000          $0
12/31
                                                                              10




         A Hypothetical Claim                           12/31
                                                    $43,000
$40
                                                                     10/06
                                         12/31
$30                                                                 $35,000
                                       $23,000

$20
                                     09/09
$10                                  $3,000

 $0     2003           2004           2005         2006           2007

      History of the Incurred Loss Development for the hypothetical claim
                 11




A Real HK case
                                                        12




III. Definition of Terms
A. Individual Claim File Estimate
1. Field adjuster establishing claim file upon notice
   of (potential) claim
2. File info
   a. Date of occurrence (accident)
   b. Date of claim
   c. Assigned lawyer
   d. Examining physician
   e. Payments-to-date
                                                        13




A. Individual Claim File Estimate
 3. Field adjuster to estimate E[future payments]
    based on
    a. Severity of potential loss
    b. Likely time to settle (ALAE will go up)
    c. Inflation between now and settlement
    d. Any recent impacts of courts or legislation
    e. Other pertinent info
 4. Case reserves =  All individual claim file
    estimates (split by line of business and accident
    year)
                                                         14




B. Gross IBNR (Reserves)
 1. Gross IBNR reserve (or bulk reserve) is total of:
    a. future development (+, -) on known claims
    b. files that are closed but may be re-open (e.g.,
       W.C.)
    c. claims incurred but not reported (pure IBNR)
    d. claims reported (to field adjuster) but not
       recorded (in head office), RBNR
                                                    15




C. Paid Loss Development
1. Paid age-to-age loss development:  cumulative
   payments on a defined set of claims between
   successive valuations (e.g., annual/quarterly)
2. Age-to-ultimate loss development:  from
   defined date (or age) evaluation to ultimate
   payment amount
3. Paid-loss development factor (L.D.F.) =
    cumulative paid @ duration j
   cumulative paid @ duration j 1
   NOTE: there are no estimates in these numbers;
   they are 100% known and 100% objective
                                                    16




D. Incurred Loss Development

1.  Same definition as above except you are using
    incurred data
    ( = pd-to-date + reserve O/S estimate) future
2. Incurred L.D.F. can be < 1
   a. if reserve estimates are conservative
   b. because of salvage or subrogation
                                                                         17




E. Salvage and Subrogation
   Salvage: e.g., if a policyholder has a car accident and the car is
    “written off,” the policyholder will receive a check for the value
    of the car at the time of claim. From that point on, the car is
    owned by the insurer. The right to any salvage value belongs to
    the insurer, and will appear in the accounts as a recovery of
    costs.
   Subrogation: e.g., if a policyholder has a house fire, the
    insurer pays for the house to be repaired or rebuilt within the
    limits of policy. If it can be shown that the fire was caused by
    the negligence of a 3rd party, the insurer has the right under
    subrogation to pursue recovery in a lawsuit against the 3rd party.
   These can lead to a less-than-one final loss-development factor.
                                                            18




F. Loss Adjustment Expenses

1.   Must reserve for future ALAE and ULAE
2.   ALAE (e.g., lawyers’ fees) are usually in claim file
     paid and incurred so are covered
3.   ULAE (e.g., head office) are allocated at year-end
     (to line of business) by formula
                                                        19




G. Fast Track Reserves
 1. Used for high freq, low severity, fast closing
    lines (e.g., auto collision)
 2. Head office actuary provides an average claim
    size based on past experience
 3. All files use this number initially
 4. Final number is entered once known (e.g.,
    claim settled)
 5. If claim file open too long, individual estimates
    take over
                                                                          20




IV. Professional Considerations
 1.   Setting reserves is not a black box computer calculation
 2.   Must have intimate knowledge of company
      a. all definitions (e.g. what is a claim)
      b. management attitude toward settling claims (i.e. fast/slow)
      c.  company’s retention limit
 3.   Must be cognizant of external factors
      a. economic inflation
      b. recent court decisions & recent legislation
 4.   Must set up data collection criteria
      a. compromise of homogeneity and statistical credibility
 5.   Review accuracy of data
 6.   Calculate reserves using more than one method
 7.   Reconciliation of different answers will narrow the range of most
      likely estimate
                                                             21




V. Checking the Data
 1. Methods are based on there being patterns in claims
    settlement
 2. Review with care any past data that do not fit pattern
 3. Calendar year action will impact the “diagonals” of
    the loss-development triangles (as seen later)
 4. Document all modifications/adjustments (and keep on
    file)
                                                                  22



VI. Loss Reserving Methods
  (There are as many loss reserving methods as there are actuaries!)

 A. Case Reserve Estimates Plus
 1. To Case file estimates add Gross IBNR or
    a. future development on known claims
    b. files that have closed but may re-open
    c. IBNR = total of pure IBNR and RBNR
 2. Method is very subjective
    a. may be used to hide profit and avoid tax or
    b. make the year profitable
 3. Could result in insolvency
                                                                          23




B. The Expected Loss Ratio Method
1.    Estimate ultimate expected loss ratio = E [LR]
2.    Then E [LR]   earned premium for fiscal period = E [$L,
      ultimate]
3.    Finally: E [Loss Reserve] = E [$L, ultimate] – [$L, pd-to-date]
4.    Again, too subjective
5.    May lead to illogical answers (e.g. if you have just taken a
      rate decrease for purely competitive reasons)
6.    At times, may be the only method available:
     a.   new line of business
     b.   gov’t regs require minimum loss ratio targets for certain
          volatile lines of business (e.g. Employee Fidelity Insurance)
     c.   can be used in conjunction with other methods (see
          Bornhuetter-Ferguson)
                                                                      24



C. The Chain-ladder or
     Loss-Development Triangle Method
1.    Historical data present as a triangle of paid or incurred
      development
2.    Create a cumulative paid or incurred triangle (Note: activity
      in row labeled Accident Year Z and column labeled
      development year t, took place in Calendar year Z+t)
3.    Calculate age-to-age loss development factors, LDF, (or link
      ratios) (see tables 4.2 and 4.3)
4.    Look for patterns in these LDF
5.    Use these patterns to create the missing half of the triangle
6.    Advantages of using paid loss
     a.   purely objective, contains no reserve estimates
7.    Advantages of incurred loss data
     a.   reserve estimate contains valuable information
                                                                          25



  C. The Chain-ladder or
       Loss-Development Triangle Method
8. Do both paid and incurred and reconcile the differences
    (ultimately they must be the same as all incurrals become paid)
9. Part of work is data review (remember calendar-year activity
    appears along diagonals of the triangle--e.g. legislative change
    or management style shift)
10. Reserve = E[ultimate paid or incurred (same)] - [Pd-to-date]
11. Note: Mean LDF (as defined in text) is a volume-weighted
    average (i.e. years of greater volume are give greater “weight”)
12. If there is consistent growth or decline in a column of LDF may
    project the trend into future values (i.e. not use a constant)
13. A LD triangle with n rows and n-l columns, creates a statistical
    model with 2n-l parameters (n-l LDF applied to n “jump-off”
    points -not good modeling!)
14. Not surprising, stability is not a characteristic of the LDF method
                                                                       26




    Stability is not a characteristic of the LDF!!
   Example 1: Increase by 10% the cumulative payments for
    accident year 2006, development year 1, from $22,253 to
    $24,478.
    The total loss reserve using 5-year average modeling
    assumption would rise 4.1%
   Example 2: The Claims Department changed its claims
    settlement philosophy for 2007 so that all losses were paid more
    promptly.
   In fact, all of the payments along the calendar year 2007
    diagonal increased by 10% (except for AY 2000, development
    year 7 which has been assumed to be fully mature).
    Logically it should lead to smaller reserve, but that resulted
    in a 9.2% larger reserve using the Chain-ladder method.
                                                                              27




     D. The Bornhuetter-Ferguson Method (BF)
1.   A combination of the E[LR] and LDF-triangle methods
2.   Adds stability to LDF-triangle method and
3.   Adjusts E[LR] as time provides more information
4.   From p.132-3 it can be shown that from the LDF method:

E [Loss Reserve] = E [$L, ultimate] ( 1 
                                             1
                                                    ), where   fULT   f j
                                            f ULT                     j

(cumulative LDF from now to )
                                                                  28




  D. The Bornhuetter-Ferguson Method (BF)

5. The BF method
   a. For each Acc Year row estimate E[LR] based on most recent
      info
   b. Then: E[$L, ultimate] = E[LR]  (Earned Premiums)
   c. Then: E[Loss Reserve] = E[$L, ultimate] ( 1 
                                                    1 )
                                                 f ULT
   d. Hence a combination of E[LR] and LDF methods
   e. BF answer will (must) lie between E[LR] answer and LDF
      answer
                                                        29
Example 4.1: You have chosen the following paid
   loss-development factors to model the lower half
   of a claims paid rectangle:

            1/0  2/1 3/2        4/3    /4
            1.41 1.22 1.16      1.08   1.04

       You are setting reserves for the annual report
   as of December 31, 2006. For accident year 2005
   you have claims paid-to-date lf $420,000 at
   report duration 1, which is December 31, 2006.
   The earned premium calculated for accident year
   2005 is $1,000,000 and the expected loss ratio
   is .600. For the 2005 accident year, determine
   the estimated loss reserve using each of the
   expected loss ratio method, the chain-ladder
   method, and the Bornhuetter-Ferguson method.
                                                                      30




  E. Estimates Split into Frequency & Severity
1. Requires for each Acc Year, E[# of claims]
   a. this data is known very rapidly (i.e. not as much gross IBNR
       on # of claims as $ Loss)
2. Given a triangle of cumulative loss payments, and a vector of
   E[# claims] for each Acc Yr, you can create a triangle called
   Cumulative Loss Payments per Claim Incurred (a severity
   triangle)
   a. usually done with “$ paid” but can be “incurreds”
   b. helpful if payments adjusted for inflation and represent
       constant $ values (more so in the late 1980’s)
3. Really good if you can create a triangle of Cumulative Closed
   Claim Files (see table 4.10)
4. This can then be transformed into %-of-claims-closed triangle to
   show the “speed of finalization” (see table 4.11)
                                                                    31




  E. Estimates Split into Frequency & Severity
5. You can thus see if the company is speeding up or
   slowing down settling claims
6. You can then “adjust” paid losses to a consistent %-
   of-claims-closed basis (see Q4.11 and do it)
7. This is important - e.g.
   a. the company decides to settle faster, but does not tell the
      actuary
   b. reserves should go down
   c. the claims-paid data suddenly show larger LDF in the last
      diagonal
   d. with larger model LDF, reserves go up - Wrong!
                                                           32




  F. Summary
1. Do more than one method and reconcile differences
2. May build some level of conservatism in, depending
   on the use of the results (e.g. solvency vs. pricing)
                                                         33




VII. Discounting Loss Reserves
 1. For the life side, discounting for time value is a
    given
 2. Historically, most P & C reserves were carried
    undiscounted (hence some implicit conservatism)
 3. Explicitly calculated provision for adverse
    deviation is probably actuarially preferable
 4. Reserves for tax purposes must now be
    discounted future development on known claims
                                                              34




VII. Discounting Loss Reserves
5. To discount
   a. create lower half of triangle = future cash flow
   b. assume payments are made at mid-pt of development
      year
   c. choose an interest rate and re-value at present value
   d. note: any given discount factor, vt, will be applied
      across a diagonal (Tables 4.12 and 4.13)
6. Now need an explicit provision for adverse deviations
                                                                35




VII. Discounting Loss Reserves
7. Issues
   a. is the mid-pt assumption valid especially for the first
      year and last year?
   b. what interest rate should I use? (answer: the net rate
      being earned by the assets backing these liabilities)
      asset-liability matching has not been the norm for P &
      C co’s
   c. it should be net of expenses
   d. how does one include unrealized capital gains?
   e. what are the tax implications?
                                                          36




VII. Discounting Loss Reserves
8. Discounted loss reserves are the correct ones to use
   in pricing (pricing actuary should discount back to
   average date of premium receipt)
9. Discounting is becoming much more common (often
   forced by tax or pricing agencies)
10.The best way to learn this stuff is to do lots of
   exercises.
11.Books are always better than movies - as well as
   power point slides!!

								
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