LOSS RESERVING

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LOSS RESERVING

• (LR)
• N Lakshmanan

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• LR is the actuarial process of estimating the
  amount of an insurance companys liabilities for
  loss and loss adjustment expenses (LAE).
• Accounting concepts
• Balance Sheet Financial position as on a date
• P L Financial performance during a period
• Income change in (assets-liabilities-
  capital)dividend owners
• BS and P L are prepared on accrual basis which
  matches revenues with their associated expenses.
• Incurred losses paid losses ending claim
  liability beginning claim
  liability
• LR estimate has a significant impact on the
  financial strength and stability of the insurer.
• Four LR basic principles

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• Technical reserves consist of
• Premium reserves
• Unearned Premium Reserves (UPR)
• Definition of URR as per GN 21 and as per
  IRDA (Assets, liabilities and SM Regulations) and
  its effect upon arriving at ASM and SR.
• Unexpired Risk Reserve (URR)

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• Claims Reserves consist of 5 elements viz.
• (i) Case reserves (CR) assigned to specific
  outstanding claims.
• (ii) Provision for future development of known
  claims (IBNER).
• (iii) Provision for reopened claims.
• (iv) Pure IBNR claims.
• (v) Claims in transit or unrecorded claims,
  though reported.
• Strictly IBNR (iv) (v). But in practice, sum
  of (ii) to (v) is called as IBNR.
• Catastrophe Reserves

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• LR process
• Data availability
• in Cum. loss dev. triangle form.
• in groups (accident year, reporting year,
  underwriting year)
• rows and columns in annual or non-annual
  intervals.
• Exploratory Data Analysis
• Analysis involves identifying and interpreting
  the patterns that exist in the data. The purpose
  is to select reasonable statistics for use with
  appropriate methods to project ultimate loss.
• Considerations Trends and changes in product
  mix, T C, RI, inflation and legal and social
  environment.
• Homogenous groups and credibility

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• Data Analysis
• Rate and smoothness of dev., presence of large
  losses, volume and anomalies in the data.
• Cum. incurred losses CIL
• Cum. paid losses CPL
• Incremental incurred losses IIL
• Incremental paid losses IPL
• CPL as a of CIL
• Cum. reported claim counts
• Cum. closed with payment claim counts Cum. closed
  with no payment claim counts
• Cum. Closed claims with or no payment as of
  reported claims
• Open claim counts

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• Average open claim amounts CIL CPL/open
  count
• change in average open CR between accident
  periods as of each dev. age - to find if CR
  are keeping up with inflationary increases.
• Average closed claims paid losses / closed with
  payment counts.
• change in average closed claims
• Closed claims during a period as a of open
  claims at the beginning of the period.
• LR Estimation Methods
• Triangular Methods (BCL)
• Cumulative paid loss development (CPLD)
• objective data, but may produce volatile results
  for immature periods.
• assumes that losses are paid at a consistent
  rate.
• Normalize the dev. history by removing the
  volume effect by finding DF.

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Age in months (in 000s)  
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Age in months
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• Cum. Incurred loss development (CILD) - changes
  in CR philosophy can distort results. IL patterns
  may be less erratic than PL patterns, especially
  for coverages which have a long payout pattern
  but for which claims are reported early and CR
  are established.
• Paid loss and incurred loss reserves estimates
  should be reconciled.
• Loss Ratio - approach multiplies earned
  premiums by an expected ult. LR to produce ult.
  loss estimate for each exposure period. This is
  useful if LD patterns are erratic, loss emerges
  very slowly or there is little loss history. It
  considers pricing assumptions in projecting loss
  and is simple. Disadvantage is actual losses are
  not recognized.

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• Claim frequency (CF)(claims per exposure) and
  severity(CS) ( loss per claim) - The product of
  exposures, ult. CF and ult. CS is estimated ult.
  losses. This is used when LD patterns are
  volatile and when CF and CS are easily
  determinable.
• Average paid loss per closed claims( with
  payment) dev. (ACPC) - Project
• No. of claims closed with payment and
• Average paid claim amount
• Total the product of the corresponding
  ultimate average paid claim amount and ult.
  number of claims closed with payment for each
  accident year
• Average incurred claims projection of the
  average amount of loss incurred per reported
  claim less claim counts closed with no payments
  (CCNP) -
• same as for ACPC above.

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• Bornhuetter Fergusen method using earned premium
  and paid loss
• LD methods may produce unreliable results for
• a new line of business with little historical
  data
• a volatile line subject to very large occasional
  losses
• cases where losses are reported over a long
  period of time and have very little loss reported
  in first 2 or 3 years ( eg. RI , XOL, TP for
  Motor)
• When loss data is erratic, BF method is
  appropriate. It offers a blend of stability and
  responsiveness in the loss reserve estimate.

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• It estimates ultimate loss by adding together
  actual reported loss with expected future
  incurred development which is equal to
• Earned premium x ELR x ( 1 1/f )
• where f Cum. incurred loss dev. Factor and
  ELR can be estimated by reviewing pricing
  assumptions, historical results or industry data
  for the line of business. It avoids over reacting
  to unexpected losses.
• It is the weighted result of incurred LD method
  and the expected loss estimate where the weights
  are based on the reciprocal of the age-
  to-ultimate factor.

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• Loss adjustment expenses.
• From 1999 as per NAIC, ALAE became Defence and
  cost containment expenses ie. for defence,
  litigation and medical cost and
• ULAE became Adjusting and other ie. all those
  not included in ALAE such as operating claims
  dept., adjuster fees, office rent and utilities.
  
• ALAE reserve estimate the ult. ratio of
  ALAE to loss and apply the same to the estimate
  of ult. losses to obtain an estimate of ALAE,
  premise being their relationship is usually
  fairly stable. But ALAE payments develop slowly
  resulting in a large leveraging impact on less
  mature periods. ALAE may be estimated separately
  from losses when experience shows that their
  patterns differ from loss payment patterns. Also,
  the ratio of ALAE to loss payments may change
  over time.

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• ULAE reserve ULAE is allocated for each line
  of business as per standard costs for each type
  of transaction and is expressed as per Rs.100 of
  paid loss, say, Rs. 13.60, the average based on
  the actuals for the previous years.
• If a certain percentage of ULAE, say, 40 is
  paid to set up an initial claim and the remainder
  is paid over the life time of the claim, the
  estimated liability for ULAE is given by
• 0.1360 pure IBNR reserve 0.1360
  (1-0.40) CR
• Evaluation of ultimate loss estimates
• Range of possible reserve estimates or best
  estimates.
• Select the estimated ult. losses among the above
  5 methods and the corresponding reserve.

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• Practical tests for reasonability
• Cum. paid losses as of selected ult. losses.
• Cum. incurred losses as of selected ult.
  losses.
• CR as of ultimate losses.
• Required reserves (ie. diff. between paid losses
  and ultimate) as of ultimate loss.
• Required reserves as of CR as this ratio can be
  stable for some lines.
• Compare ultimate losses with the earned premium
  or exposures.
• AY Sel. ult. Earned prm. Ult.
  LR ELR Give feedback to underwriting
  dept. to take corrective action.

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• Another benchmark is average ult. claim size or
  severity. We expect severity to trend with
  inflation. Compare selected ult. losses to the
  projected number of claims net of claims with no
  payment.
• AY Sel.ult. Ult. claims no. Ave. claim
  Change in Ave.
• Claim frequency Number of claims / exposure
  can be used as a reasonableness check for the
  projected no. of claims.
• AY Ult. cl. no. Earned prm. Freq.
  Change in Freq.

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• Monitoring Results
• Compare projections of expected development over
  next year for paid loss, CR, IBNR counts and the
  no. of claims closed with payment with the
  corresponding actuals to give confidence in the
  analysis and understanding of the situation.
• Reserve Discounting
• Discount is very sensitive to rate of interest
• Type of investments held and expected return on
  them determine the appropriate rate of discount.
• Effect of discounting is to release profits early
  and prepone taxes.
• Reserve Estimate Ranges
• It is difficult to obtain one single point
  estimate of the LR liability. As we estimate the
  mean of a stochastic process, the actual result
  will always differ from the estimate. Hence, a
  range of results and a statement of confidence
  that the observed reserve liability at final
  development will be within the stated range are
  preferable.

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• Conclusion
• Accurate LR and LAE reserve are critical to
  companys performance to enable strategic and
  operational decisions.
• Feedback for improvement of underwriting, pricing
  and claims processing procedures.
• Different methods for determining profitability
  of a line of business or for statutory reporting
  
• Reasonability checks for ultimate losses.
• Frequent monitoring of projections at periodic
  intervals necessary.

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• THANK YOU