1. Importance of Accurately Estimating Unpaid Claims
    3 Viewpoints
    • 1. Internal Management
    • 2. Investors
    • 3. Regulators
  2. Importance of Accurately Estimating Unpaid Claims
    Internal Management
    • 1. Accuracy essential for proper decision making
    • 2. Pricing
    • (a) Inaccurate estimates can threaten fi nancial condition of insurer
    • 3. Financial results often drive decisions
    • (a) Underwriting - increase business, exit market
    • (b) Strategic - reinsurance needs
    • (c) Financial - capital management
  3. Importance of Accurately Estimating Unpaid Claims
    • 1. Inaccurate reserves can cause misstated balance sheets and income statements
    • 2. Inaccurate reserves can lead to misleading fi nancial metrics
  4. Importance of Accurately Estimating Unpaid Claims
    • 1. Rely on financial statements to supervise
    • 2. Inadequate reserves may result in misstatement of true fi nancial position
    • (a) May delay regulator intervention and not allow them to help insurer
  5. Further Requirements for Accurate Reserves
    • 1. State Law
    • 2. NAIC - National Association of Insurance Commissioners
    • 3. Other Examples
  6. Further Requirements for Accurate Reserves
    State Law
    • 1. Many tie legal requirements for unpaid claim estimation to responsibilities of actuary
    • 2. Role of Appointed Actuary created through insurance legislation around the world
  7. Further Requirements for Accurate Reserves
    NAIC Major characteristics of 1970's and 1990's
    • 1. Mid 1970's
    • (a) Increasingly litigious environment
    • (b) Many insolvencies involving inadequate claim reserves
    • (c) NAIC recommended companies include claim reserve opinions with annual statements
    • 2. 1990's
    • (a) NAIC required most P&C insurers to get Statement of Actuarial Opinion signed by a quali fied actuary
    • (b) 1993 - Title Appointed Actuary used because must be appointed by Board
  8. Further Requirements for Accurate Reserves
    Other Examples
    • 1. Many state insurance departments require actuarial opinions for captives, self-insurers, and self-insurance pools
    • 2. Canada
    • (a) Insurance Companies Act requires all federally regulated insurers to have Appointed Actuary
    • (b) Responsibilities include valuation of actuarial and other policy liabilities of company
    • 3. Australia and Slovenia also require Appointed Actuaries
  9. Ranges of Unpaid Claim Estimates
    • 1. Difficult to obtain single estimate of claims liability - di fferent methods produce varying estimates
    • 2. Range of estimates and statement of confi dence level
    • (a) Valuable to management, regulators, policyholders, investors
    • (b) However, balance sheet requires point estimate
    • i. Some countries (e.g., U.K., Australia) insurers required to book at 75 % confi dence level
    • 3. ASOP 43 defi nes the actuarial central estimate as an estimate that represents an expected value over the range of reasonably possible outcomes
  10. Di fferences in Coverages and Lines of Business Around the World
    • 1. Di fferences in names used (e.g., automobile, car, motor insurance)
    • 2. Some coverages may not exist in other countries or operate diff erently (e.g., WC, med mal)
  11. Key Terminology
    Risk bearer for P&C exposures
  12. Key Terminology - Reserves
    • 1. ASOP 43 - reserve is amount booked in a fi nancial statement
    • 2. Diff erent estimation techniques will likely generate diff erent unpaid claim estimates
    • (a) Also will likely change from one valuation date to another
    • 3. Carried reserve - amount reported in a published statement
    • 4. Important reason to separate IBNR is to test adequacy of case outstanding over time
    • 5. Important to completely understand diff erent types of data provided (Ch. 3)
  13. Key Terminology - Reserves
    ASOP 43: Unpaid claim estimate; Unpaid claim estimate analysis
    • Unpaid claim estimate - actuary's estimate of the obligation for future payment resulting form claims due to past events
    • Unpaid claim estimate analysis - process of developing estimate (a.k.a. reserving)
  14. Key Terminology - Reserves
    Five components of unpaid claims estimate
    • 1. Case outstanding on known claims (estimate of unpaid established by claim dept)
    • 2. Provision for future development on known claims
    • 3. Estimate for reopened claims
    • 4. Provision for claims incurred but not reported (pure IBNR)
    • 5. Provision for claims in transit (reported but not recorded)

    *Refer to sum of last 4 as the broad defi nition of IBNR
  15. Key Terminology
    Ultimate Claims
    • 1. Total dollar value after all claims are settled and closed w/o any chance of reopened
    • 2. Sum of paid, IBNR and case outstanding
  16. Key Terminology
    Experience Period
    Years included in a specifi c technique for estimating unpaid claims
  17. Key Terminology
    Reporting or development of claims and claim counts over time
  18. Claims Professionals
    • 1. Employee of insurer: large insurer generally maintains internal claims departments with many adjusters
    • 2. Third-party claims administrators (TPA): may be hired by small to mid-sized commercial insurers or self-insurers to handle a specifi c book of claims
    • 3. Independent adjuster (IA): handle individual claim or group of claims; may be needed for specifi c type of claim, particular region, or in disasters
  19. Claim is Reported
    • 1. Estimation process begins when insured first reports a claim or notice of event
    • 2. Is claim covered? (eff ective date of policy; date of occurrence; terms and conditions of policy; ...)
    • 3. Estimate reserve: tabular value or formula; important to recognize estimate based on information known at the time: as additional information becomes available, estimate may change
  20. Establishing Case Outstanding - several approaches
    • 1. Claim
    • (a) Best estimate of the ultimate settlement value including consideration of inflation
    • (b) Set at policy limit
    • (c) Seek advice of legal council on probability it will settle for various amounts (set at mode or mean)

    • 2. Claim adjustment expenses
    • (a) Some insurers only set case outstanding for the claim amount
    • (b) When claim adjustment expense case outstanding is set
    • i. Claim and claim-related expenses may or may not be set separately
    • ii. Amount may include only ALAE or both ALAE and ULAE

    3. Salvage and subrogation case outstanding may or may not be established

    • 4. Reinsurance recovery case outstanding is relatively straight-forward
    • (a) Proportional -> ceded case outstanding based on reinsurer's share
    • (b) Excess of loss -> total case outstanding less insurer's retention
  21. The Life of a Claim
    Diff erent types of claim transactions over the life of the claim
    • 1. Establishment of the initial case outstanding estimate
    • 2. Notifi cation to reinsurer if claim expected to excess retention
    • 3. Partial claim payment to injured party
    • 4. Expense payment for independent adjuster
    • 5. Change in case outstanding estimate
    • 6. Claim payment
    • 7. Takedown of case outstanding and closure of claim
    • 8. Reopen claim and establish new case outstanding estimate
    • 9. Final payment for defense litigation
    • 10. Closure of claim
  22. The Life of a Claim
    Incurred Loss
    • (a) CY Inc Loss = Paid Loss + End Case Res - Beg Case Res
    • (b) AY Inc Loss = Paid Loss + End Case Res
    • (c) Total Inc Loss = Paid Loss + End Tot Res - Beg Total Res
  23. 4-phase approach to the process of estimating unpaid claims
    • 1. Exploratory analysis of the data
    • (a) Identify key characteristics and possible anomalies
    • (b) Balancing data to other verifi ed sources
    • 2. Apply appropriate techniques for estimating unpaid claims
    • 3. Evaluating the conflicting results of the various methods
    • (a) Attempt to reconcile or explain the diff erent outcomes
    • (b) Projected ultimate amounts evaluated in contexts outside their original frame of analysis
    • 4. Monitoring projections of claim development over subsequent calendar periods
    • (a) Deviations of actual development from projected one of most useful diagnostic tools in evaluating the accuracy of unpaid claim estimates
  24. Sources of Data
    • 1. Large insurers often rely solely on int data (may need ext data for new lob or terr)
    • 2. Small insurers are more limited with the avail int data (small vol w less cred, systems limitations)
    • 3. Ext sources of info:
    • US: ISO, NCCI, RAA, Best, NAIC;
    • Canada: Best, IBC, RRC, MSA
    • 4. Many insurers use a combination of ext and int data
    • 5. Ext data used for: tail dvpmt, trend rates, expected CR, evaluating and reconciling results of various methods
    • 6. Potential problems with ext data: may be misleading or irrelevant due to differences relating to insurance products, CO practices, operations, geog, mix of b
    • 7. External data typically used only as a fallback where internal data not credible
  25. Homogeneity and Credibility of Data
    • 1. Subdividing experience into groups with similar characteristics may improve accuracy of reserve estimates
    • 2. Group claims by lines and sublines which display similar traits
    • 3. Actuaries focus on key characteristics
    • 4. May also group by policy limits to achieve similar claims attributes within block of business
    • 5. Goal for actuary to divide data into sufficiently homogeneous groups without compromising credibility of data
  26. Homogeneity and Credibility of Data
    Actuaries focus on key characteristics
    • 1. Consistency of coverage triggered by the claims in the group (laws, terms, claims handling)
    • 2. Volume of claim counts in group
    • 3. Ability to develop an appropriate CO estimate from earliest report through the life of the claim
    • 4. Settlement or payment patterns (length of time to settle claim once reported)
    • 5. Likelihood of claim reopening
    • 6. Severity
  27. Data: Large Claims Treshold
    • 1. Presence of unusually large claims can distort some estimation methods
    • 2. May exclude large claims, apply methods to remaining data, add large claims using case estimate and provision for IBNR
    • 3. Determination of size criteria not exact
    • (a) May vary by LOB, territory, and even between analyses
    • (b) Judgement is critical and considerations include
    • i. Number of claims over threshold
    • ii. Size of claim relative to policy limits
    • iii. Size of claim relative to reinsurance limits
    • iv. Credibility of internal data regarding large claims
    • v. Availability of relative external data
    • (c) May seek advice from reinsurance department
  28. Verifi cation of the Data
    • 1. SOPs require verifi cation that data is reliable and sufficient for intended purpose
    • 2. Data review may include:
    • (a) Consistency with fi nancial statement data
    • (b) Consistency with prior data
    • (c) Data reasonableness - e.g., may need to question large negative paid
    • (d) Data de finitions - see previous section
    • 3. Documentation of verifi cation process and fi ndings should also occur:
    • (a) May include discussions with external auditors and reliance on their work
  29. Organizing the Data
    5 Key Dates
    • 1. E ff Dates - beginning and ending dates of the policy term (UW date)
    • 2. Accident Date - date on which the loss occurred. May be ambiguous w claims-made
    • 3. Report Date - date on which the loss is fi rst reported to an insurer. May be split into notification, reported and recorded.
    • 4. Accounting Date - date used to defi ne the group of claims to be included in the liability estimate; unpaid claims as of a given date
    • 5. Valuation Date - date as of which the evaluation of the loss liability is made. Defi nes the point in time through which all transactions included for group of claims. Can be before, after or the same as the accounting date
  30. Aggregation by CY
    • 1. Transactional data
    • 2. Uses: aggregation of exposures, diagnostic testing when analyzing AY claims data
    • 3. Premiums: EP = Written + Beginning UEPR - Ending UEPR
    • 4. Adv: no future dvpmt; readily available - most fi nancial reporting on a CY
    • 5. Disadv: inability to address the critical issue of dvpmt; very few techniques based on CY
    • 6. However, CY exposures are frequently used in techniques with AY claims
  31. Aggregation by AY
    • 1. Claims grouped according to date of occurrence
    • 2. Most common grouping of claims data for the actuarial analysis of unpaid claims
    • 3. CY exposures often used with AY claims: CY EP approx match AY claims (exact for self-insr)
    • 4. Adv: grouping easy to achieve and understand; shorter time frame than PY: reliably estimable sooner; numerous benchmarks available; valuable when chg due to economic or regulatory forces or cat
    • 5. Disadv: potential mismatch btwn claims and exposures; incl claims from policies underwritten and prices at more varied times then PY
  32. Aggregation by PY or UY
    • 1. Sort claims by year in which policy was written
    • 2. Adv: true match btwn claims and exposures; can be very important when UW or pricing chg occur (prices, ded, mix of b)
    • 3. Disadv: extended time frame; difficult to understand and isolate eff ect of a single large event
  33. Aggregation by RY
    • 1. Group claims according to date of report to the insurer: Claims-made coverage is dependent on the report date
    • 2. Actuaries use to estimate the ultimate value of known claims: Can also be used to test adequacy of CO on known claims over time
    • 3. Adv: nbr of claims is fi xed at close of the year: results in more stable data and development patterns then AY approach
    • 4. Disadv: only measure development on know claims and not pure IBNR (frequently the more difficult part to estimate)
  34. Meeting with Management
    Understanding the Environment
    • 1. Internal - specifi c circumstances existing within insurer's organization
    • 2. External - economic, social, legal, regulatory
    • 3. Claims reporting and payment patterns, frequency, and severity call all be altered by changes in classes of business written or geographical focus, policy provisions (limits and ded), reinsurance arrangements, etc,
    • 4. Consultant meetings usually less frequent and formal (annual reviews)
    • 5. Collection process includes both a review of quantitative data and discussions with key members of insurer's claim and UW
  35. Development Triangle
    • Development triangle - table that shows changes in value of various cohorts over time
    • Analyze many di fferent values: rpt claims, paid claims, claim-related expenses, rpt claim counts
    • One of most common tools that actuaries use to organize data in order to identify and analyze patterns in historical data
  36. Ratio of Paid-to-Reported Claims
    • Examines consistency of paid claims relative to reported claims
    • Test for changes in CO adequacy and settlement patterns
    • No changes in ratio doesn't mean changes aren't occurring: speed-up in claims closure and case strengthening, may be o ffseted by increasing rpt claims
    • Downward trend could result from decreasing paid claimsor increasing case adequacy
  37. Ratio of Paid Claims to On-Level Earned Premium
    Helps provide insight as to whether there was a speed-up in claims payment or possibly deterioration in underwriting results
  38. Claim Count Triangles
    Three Important Items that actuary must understand
    • 1. Reopened claims
    • 2. Closed with no payment (CNP)
    • 3. How are claims classi fied with only expense payments
  39. Ratio of Closed-to-Reported Claim Counts
    • Review when suspect a change in settlement rate of claims
    • Forces that could result in change in ratio of closed-to-reported claim counts
    • 1. Large cat has potential to temporarily limit insurer's operations
    • 2. Change in guidelines for the establishment of a claim
    • 3. Decrease in the statute of limitations (tort reform)
    • 4. Introduction of a new call center to handle claims: Could a ffect both the numerator and denominator
  40. Use of Average reported claim triangle detect possible changes in case adequacy
    • Not as valuable as average case outstanding: Since reported claims include paid claims which can mask changes
    • However for some insurers, open counts are not available
  41. Observations regarding Average Reported Claim and Average Paid Claim Development
    • Expect to see changes down columns for inflationary forces only
    • i. Changes in average reported greater than assumed inflation may be due to higher paids or stronger case outstanding
    • ii. Other factors may aff ect severity trends
    • Changes in policy limits purchased, geographic mix, type of insureds, definition of claim counts
    • When looking at average paid, need to ask whether there has been change in type of claim being settled at particular ages
    • i. Could aff ect selection of estimation techniques and claim projection factors
  42. Observations regarding Average Case Outstanding Development
    • Important that actuary understands dynamics of insurer
    • i. Changes in case outstanding practices, policies, philosophy, sta ff, senior management?
    • ii. Avg case outstanding also aff ected by changes in mix of business
    • Case outstanding is generally increasing by more than the inflation rate
    • However, must consider diff erent mix of claims: E.g., If smaller claims settling more quickly, will increase the average case outstanding
  43. 3 Components of Ultimate Claims
    • 1. Cumulative paid claims
    • 2. Case outstanding
    • 3. IBNR

    Relationships among components vary by LOB, Jurisdiction, Time interval
  44. Components of Ultimate Claims
    Short-Tail vs. Long-Tail
    • Short-tail lines
    • - Paid and case typically are a high proportion of ultimate claims at early maturities
    • - Short time period associated with reporting and settlement
    • - E.g., auto physical damage and property
    • Long-tail lines
    • - Lengthy period of time associated with reporting and settlement
    • - E.g., med mal, WC, GL
    • - IBNR can make up large portion at early stages
  45. Specifi c areas where actuarial judgement is required
    • 1. Determining optimal combinations of kinds of claims data to be used in estimation
    • 2. Assessing eff ect of changes in an insurer's operations on the claims data
    • 3. Adjusting claims data for influences of known and quanti fiable events
    • 4. Evaluating the strengths and weaknesses of various estimation techniques
    • 5. Making the fi nal selection of the unpaid claim estimate
  46. Assumptions in CL Technique
    • 2 Key Assumptions
    • 1. Future claims' development is similar to prior years' development
    • - Rel chg in a given year from one evaluation to next is similar to the rel chg in prior years
    • 2. Implicitly assumes claims observed for an immature AY tell you something about claims yet to be observed
    • 4 Additional Assumptions
    • 1. Consistent claims processing
    • 2. Stable mix of claims types, policy limits, reinsurance retention limits
  47. 7 Steps of CL Technique
    • 1. Compile claims data in a development triangle
    • 2. Calculate age-to-age factors (a.k.a. report-to-report factors or link ratios)
    • 3. Calculate averages of the age-to-age factors
    • 4. Select claim development factors (a.k.a. age-to-age or loss development factor)
    • 5. Select tail factor
    • 6. Calculate cumulative claim development factors
    • 7. Project ultimate claims
  48. CL Technique: When Does it Work?
    • 1. When key assumptions fail to hold
    • 2. Changes in insurer's operations (claims processing systems, claims mgmt philosophy, deductibles, insurer retention)
    • 3. Works best when presence or absence of large claims does not greatly distort the data
    • 4. Insufficient volume of credible data: new LOB, new terr, or small insurer
    • 5. Works well with high-freq, low-sev lines w stable and timely reporting, especially where claims evenly spread throughout the AY (otherwise potential for significant diff in avg claim maturity)
    • 6. Leveraged eff ect of large claim development factors result in projections that are very sensitive to current value of claims (often seek alternative techniques)
  49. CL Technique vs Changing Environment
    • 1. Inc CR, stable CO adeq: no changes in age-to-age factors -> responsive
    • 2. Stable CR, inc CO adeq: age-to-age factor not responsive -> paid responsive, rpt overstates
    • 3. Inc CR, inc CO adeq: paid responsive, rpt overstates
  50. Expected Claims Technique
    Key Assumption
    • Unpaid claims can better be estimated based on an a priori estimate than using experience observed to date
    • a) Total claims are a function of a priori estimate and not actual claims activity to date
    • b) Experience reported to date may provide little info about ultimate claims
  51. Expected Claims Technique
    Common Uses
    • Commonly used in lines with longer emergence and settlement patterns
    • Insurer enters a new line of business or new territory
    • Operational or environmental changes make recent historical data irrelevant for projecting
    • CL method is not appropriate for less mature periods due to highly leveraged development factors
    • Data is unavailable for other methods
    • Expected claims are a critical component of several other methods (e.g., BF, Cape Cod)
  52. Expected Claims Technique
    Mechanics of the Expected Claims Technique
    • 1. Simple Approach: Ult claims = selected expected CR * EP - Implicitly relies on accuracy of pricing and UW
    • 2. Complex Approach: Complex simulation model projecting expected claims
    • 3. Exposure-based approach: predetermined exposure base * selected measure of claims per unit of exposure
    • - Challenges: determine appropriate exposure base, estimate measurement of claims relative to exposure base
  53. When the Expected Claims Technique Works
    • Used when:
    • 1. Entering a new LOB or terr: use insurance industry benchmarks for CR, PP
    • 2. When cumulative claim development factors are highly leveraged
    • 3. When insurer has experienced signifi cant chg: must reliably estimate CR given conditions
  54. Expected Claims Technique
    Advantages & Disadvantages
    • Advantage:
    • Maintaining stability over time

    • Disadvantage:
    • Lack of responsiveness to recent experience
    • Ignores actual claim experience and thus ignores when it diff ers from initial expectations
    • However, actuary may make it more responsive when data is adjusted judgementally to incorporate changing conditions before they are fully in the data
  55. Expected Claims Technique vs Changing Environment
    • 1. Inc CR, stable CO adeq: lacks responsiveness: unless actuary changes expected CR -> understate
    • 2. Stable CR, inc CO adeq: no e ffect on the expected CR -> accurate
    • 3. Inc CR, inc CO adeq: understate by same amount as 1
  56. BF Technique Definition
    • BF technique is a blend of the CL and expected claims techniques
    • i. Splits ultimate claims into actual rpt and expected unrpt
    • ii. As experience matures, more weight given to actual claims
    • iii. Credibility = Z = 1 / CDF
  57. BF Technique
    Key Assumptions
    • Unrpt claims will develop based on expected claims, i.e., claims rpt to date give no info about claims yet-to-be reported
    • Reporting and payment patterns are the same as selected in the development method
  58. Mechanics of BF Technique
    • Ult Claims = Actual Rpt Clms + Expected Clms * (1 - 1 / CDFult)
    • Using Mack notation, UBF = Ck + qkU0
    • % unrpt also referred to as IBNR factor
    • % unrpt is estimated using the selected development factors
  59. When the BF Technique Works
    • Frequently used for long-tail lines of insurance, particularly for most immature years due to highly leveraged CDFs
    • Used when data is extremely thin or volatile or both (new LOB or terr); may rely on benchmarks for dvpmt patterns and expected CR
    • Can be useful for short-tail lines: IBNR can be set at a multiple of the last few months' EP
  60. Advantage of the BF Method
    • Random fluctuations at early maturities do not signi cantly distort the projections
    • An exceptionally large claim should not be allowed to distort the IBNR reserves
  61. BF Technique vs Changing Environment
    • 1. Inc CR, stable CO adeq: lacks responsiveness; must chg expected CR; Paid BFworse than Rpt BF -> understates
    • 2. Stable CR, inc CO adeq: Rpt BF method overstates the IBNR (inc in CDFs lead to inc in % rpt). Note: the overstatement is less for the rpt BF than for rpt dvpmt; Paid BF is una ffected
    • 3. Inc CR, inc CO adeq: Paid BF understates IBNR (lack of responsiveness to inc CR); Rpt BF has two factors working against each other
  62. Benktander Technique (iterative BF)
    • Credibility-weighted average of BF and development technique
    • - Advantage - more responsive than BF and more stable than development technique
    • - Uses BF estimate as the initial expected losses to run BF again
    • - Can be useful for short-tail lines
    • - Benktander always gives greater credibility than BF does to the development technique
    • - When no chg in underlying claim development patterns, expect Benktander to be more responsive than BF
    • - When claim dvpmt patterns are changing, Benktander may not produce most appropriate estimate
  63. Cape Cod Technique (Stanard-Buhlmann)
    • Derivation of expected CR is obtained from the rpt claims rather than judgmental as in BF
    • Assumption: Unrpt claims will develop based on expected claims
    • Uses: Reinsurers, all lines of insurance
    • Mechanics: Ult Claims = Actual Rptd + Expected Unrptd
    • SB ECR = Σ(Rpt Claims) / Σ (Adj EP * %Rpt)
    • Denominator = "used-up premium"
  64. When the Cape Cod Technique Works
    • Advantage: rdm fluctuations at early maturities do not signi ficantly distort the projections (still some eff ect due to derivation of ECR)
    • Not necessarily appropriate as BF when data is extremely thin or volatile or both (ECR based on rpt)
    • Ideally, premiums are adj to an on-lvl basis and claims adj for trend & benefi t-lvl chg
    • - However, info may be unavailable: take into consideration when making fi nal selections
  65. Cape Cod Technique vs Changing Environment
    • 1. Inc CR, stable CO adeq: more responsive than BF because of the increased ECR, still understates IBNR, but not by as much as EC or BF
    • 2. Stable CR, inc CO adeq: overstates the IBNR by more than BF
    • 3. Inc CR, inc CO adeq: two factors working against each other
  66. Frequency-Severity Techniques Definition
    • Freq-Sev estimates provide add'l estimates of unpd clms & help in understanding the drivers in claims activities
    • Method: Project ult clms by mult est ult nbr of claims by est ult avg value
    • Adv: examine trends and patterns in clm emergence and settlement, and average values (chg in operations, philosophy, or mgmt)
    • Can also be important to validate or reject findings from other projection techniques
  67. Freq-Sev Approach #1
    CL Technique with Clm Cnts and Sev
    • Assumptions: consistent def of clm cnt, reasonably homogenous clm cnt, past pred fut
    • Method:
    • 1. Project and select ult clm cnt
    • 2. Project ult sev
    • 3. Project ult clms = proj ult sev * proj ult clm cnt
    • 4. Develop unpd clm estimate
  68. Freq-Sev Approach #2
    Incorporation of Exposures and Inflation
    • Assumptions: Trend rates are used (economic and social inflation) (vary by LOB, sub-cov)
    • Mechanics:
    • 1. Use hist data to project ultimates for the latest two AYs
    • 2. Determine appropriate freq for latest two AYs (trend clm cnt and exposures)
    • 3. Project ult sev: select latest severity and trend back to estimate prior severity
    • 4. Proj ult clms = exposures * sel freq * sel sev
  69. Freq-Sev Approach #3 - Disposal Rate Technique
    • 1. Disposal Rate = AY cumulative closed clm cnt at age x / selected ultimate AY claim count
    • 2. Project clm cnt by AY and maturity using sel DR; project incr clms closed
    • 3. Produce incr pd sev, adjust sev to common time period
    • 4. Select trend rate
    • 5. Calculate sev by maturity AY
    • 6. Proj clms = clm cnt * sev
    • 7. Proj incr clms = Incr closed clm cnt * incr pd sev
  70. When Freq-Sev Techniques Work
    • Advantages
    • - greater insight into the claims process
    • - may be used with pd clms data only; Case reserving philosophy or procedures will not aff ect results
    • - ability to explicitly reflect inflation in the projection
    • Disadvantages
    • - highly sensitive to the inflation assumption (test sensitivity)
    • - data needed may be unavailable
    • - chg in def of clm cnt or clm processing
    • - rely on mix of claims to be relatively consistent
  71. Enhancements for Freq-Sev Techniques
    • 1. Consider the influences of seasonality on frequency and severity inflation
    • 2. Understand the data underlying the analysis
    • 3. For lines where reopened claims are more prevalent, freq-sev may not be appropriate
    • - May choose to segregate reopened claims and analyze separately
  72. Freq-Sev Projection as Input to BF Technique
    • Projected ult clms from freq-sev technique often valuable as an alternative expected claims estimate for BF technique
    • - Actuary may feel more comfortable with freq and sev selections than an ECR
  73. CO Approach #1 - Key Assumptions
    • Claims recorded to date will continue to develop in a similar manner in the future
    • Past is indicative of the future
    • Claims activity related to IBNR is related consistently to claims already reported
    • - i.e., development on known claims versus pure IBNR
  74. CO Approach #1 - Common Uses
    • Second assumption limits use
    • Method appropriate when most clms rpt in 1st accident period
    • - Works well with claims-made coverage and report year analysis
  75. CO Approach #1 - Mechanics
    • Incr pd clms in each interval related to CO at beginning of period
    • 1. Calculate ratios of incremental paid at x to CO at x-12
    • 2. Calculate ratios of CO to the previous CO
    • 3. Project future CO
    • 4. Project future incremental paid
    • 5. Ultimate claims equal sum of incrementals
    • Challenge of technique is selection of the "to ultimate" ratios (no benchmarks)
  76. CO Approach #1 - When Does it Work
    • Assumption that future IBNR is related to claims already reported doesn't hold true for many P/C lines
    • Infrequently used and lack of benchmarks, lack of intuitive sense and experiential knowledge as to appropriate ratios
  77. CO Approach #2 - Introduction
    • Assume only data available for our self-insurer is case outstanding
    • - Not particularly common, but can occur
    • - More likely for older years
    • - Can arise following times of transitions, such as mergers and acquisitions
    • - May not have paid information prior to commencement of self-insurance program
  78. CO Approach #2 - Common Uses
    • Not used extensively by actuaries
    • Used most often due to absence of other reliable claims data
  79. CO Approach #2 - Mechanics
    • Not able to create pd or rpt clm dvpmt triangles, rely on industry benchmark
    • Project estimates of unpaid claims
    • - Apply case outstanding development factor (CODF) to case outstanding
    • - Image Upload 2
    • - Resulting case development factor includes provisions for CO and IBNR
    • - Note: this will project unpaid claims, not ultimate claimss
  80. CO Approach #2 - Potential Limitations
    • Benchmarks may prove to be inaccurate
    • Generally inappropriate for more recent, less mature years
    • Increased variability of results related to highly leveraged development factors
    • Individual large claims present in CO data can distort projections
  81. Berquist-Sherman Techniques
    Reacting to a Chging Env through Data Selection and Rearrangement
    • - Use earned exposure instead of claim counts
    • - Substitute PY for AY when limits or deductible change in successive yrs
    • - Substitute RY for AY when shift in the social/legal climate which causes sev to more closely correlate with the report date
    • - Substitute accident quarter for AY when growth of earned exposures shifts avg accident date
    • - Subdivide loss experience into more homogenous groups: major chg in the composition of business by state, subline, terr
  82. Berquist-Sherman Techniques
    • 1. Choose diagonal from which you'll calculate other values (Adv of latest: will remain the same in adj / unadj triangles)
    • 2. Select an annual sev trend to adjust avg case
    • 3. Restate avg CO triangle by trending back from latest diagonal
    • 4. Adjusted Rpt Clms = Adj Avg Case x Num of Open Claims + Unadj Paid
    • 3. Perform reported claim dvpmt technique on adjusted data
  83. Defi nition of Salvage & Subrogation
    • Salvage- amnt insurer is able to collect from sale of damaged property acquired when paying insured for a total loss
    • Subrogation - insurer's right to recover the amnt of claim payment to a covered insured from a third-party responsible for the injury or damage
    • Important that actuary understands insurer's practices with respect to S&S
    • Need to know whether paid claims are recorded net or gross of these recoveries
  84. How recoveries can be reported
    • - Some insurers keep detailed CO estimates and pmts for recoveries
    • - Some insurers combine claims data for all types of recoveries
    • - Some insurers record only payments and do not estimate CO
    • - Some insurers treat recoveries as negative claim payments
    • When data is available, actuaries frequently use the development technique to quantify
    • - Salvage, commonly in property, tends to be fast reporting and settling
    • - Subrogation, commonly in liability, often paid well after underlying claims are paid; Resulting in CDFs < 1 for older maturities for some lines of business
  85. DCC and A&O
    • NAIC promulgated two new categories of claim adjustment expenses effective January 1, 1998 for U.S. insurers reporting on Schedule P of the Annual Statement
    • DCC
    • - Defense and cost containment
    • - Includes all defense litigation and medical cost containment expenses, whether internal or external to insurer
    • A&O
    • - Adjusting and other
    • - Includes all claim adjusting expenses, whether internal or external to insurer
  86. Estimation Techniques for ALAE
    • Development methods used can also be used for DCC
    • Key factors on whether development methods can be used for adjustment expenses
    • - Whether or not sufficient detail is available
    • - Whether the expenses tend to track accident or are more dependent on calendar year
    • ULAE or A&O are often related to the size of insurer's claims department
    • - Less closely related to claims
  87. Ratio of paid ALAE-to-paid claim dvpmt - mult approach
    • Method: Project ult clms, dvlp ratio of pd ALAE-to-pd clms
    • Assumption: Relationship btwn ALAE and claims is relatively stable
    • Advantages: Recognizes relationship btwn ALAE and claims; not highly leveraged; easy to interject actuarial judgment
    • Disadvantages: Any error in estimate of ult clms could a ffect estimate of ult ALAE; ALAE spent on claims with no pmt
  88. Ratio of paid ALAE-to-paid claim dvpmt - additive approach
    • Method: Project ult clm; develop ratio of paid ALAE-to-paid clms: take di ff btwn ratios at successive ages; Age-to-ultimate factor is then the cumulative sum from age to ultimate
    • Advantage over multiplicative approach: more stable when ratios are very small at early maturities
  89. Choosing a Technique for Estimating Unpaid ALAE
    • Need to conduct similar evaluation analyses as for claims
    • Choice of technique depends primarily on
    • - Types of data available
    • - Credibility of data
    • - Understanding as to how insurer's environment a ffects various techniques
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