Here I've compiled outlined notes of the CAS Exam 5 text on Reserving by Friedland. It is my hope that these notes be of some use to other CAS candidates or curious students in gaining more insight and understanding across a spectrum of topics within insurance, from the claims process to various basic techniques for estimating unpaid claims.
The contents (whose formatting will be fixed) are as follows. Additionally, my hand-written notes on which this post is based will also be posted.
[A] Introduction
1. Overview
2. The Claims Process
[B] Information Gathering
3. Understanding Data Types Used to Estimate Unpaid Claims
4. Meeting with Management
5. Development (Loss)
6. Development Triangle as Diagnostic Tool
[C] Basic Techniques for Estimating Unpaid Claims
7. Development Technique (using CDFs)
8. Expected Claims Technique
9. Bornhuetter-Ferguson Technique
10. Cape Cod Technique
11. Frequency-Severity Techniques
12. Case Outstanding Development Technique
13. Berquist-Sherman Techniques
14. Recoveries: Salvage & Subrogation & Reinsurance
15. Evaluation of Techniques
[D] LAE
16. Estimating Unpaid Allocated Claim Adjustment Expenses
17. Estimating Unpaid Unallocated Claim Adjustment Expenses
Ch 1 – Overview
- Insurers sell “promise to pay” in the event of an occurrence covered by policy
- Accurate estimate of unpaid claims is very important for:
Internal Management – Helps guide appropriate decisions {pricing, underwriting, strategic & financial decision}
Inadequate estimate of unpaid claims:
- Risks future solvency of the insurer; lower estimate -> lower rates -> insufficient reserves -> larger market share -> problem gets worse
§ Excessive estimate of unpaid claims:
· May drive insurer to unnecessarily increase rates -> less market share -> loss of profit opportunity (premium revenue) -> negatively impacts financial strength of insurer
§ Inaccurate estimate of unpaid claims:
· Hurts ability to judge whether to increase business or exit/abandon certain areas and markets
o Investors - “key financial metrics” can be misled
o Regulators – Inaccurate estimates may impede insurance regulators’ ability to step in promptly to help the insurer regain its strength
o State Law – requires insurers to keep the amount estimated of unpaid claims “in the aggregate”
o (NAIC) National Association of Insurance Commissioners – requires most P&C insurers to obtain a “statement of Actuarial Opinion” signed by a qualified actuary (“Appointed Actuary”) -> reasonableness of carried statutory loss & loss adjustment expense (LAE) reserves
Definitions:
· captive insurer – limited purpose, licensed insurance company; insure/reinsure risks of captive’s owners
· self-insurance – wide range of risk financing arrangements where companies pay all/most of their own losses
· underwriting pools – created in some jurisdictions to provide coverage for specific exposures, such as residual market automobile or aviation, across the insurance industry
Adjustment Expenses (United States):
- DCC (Defense & Cost Containment) – defense litigation & medical cost containment expenses, internal and external
- A&O (Adjusting & Other) – all claims adjusting expenses, internal or external
Note: Estimation methods will usually provide different & varying outcomes of unpaid claim estimates. Estimating mean of stochastic process -> actual unpaid claims amount almost always different from estimate
“Insurer’s Balance Sheet” – requires insurer to record a single point estimate of the unpaid claims
- Confidence interval of true unpaid claims amount is useful to management, regulators, policyholders, investors, and general public, but the REQUIREMENT is the “single point estimate”
“Actuarial Central Estimate” (ASOP 43: Actuarial Standard of Practice)
- Expected value over the range of reasonably possible outcomes
Coverages (AKA) Lines of Insurance
- Accident Benefits
o “no fault” coverage (ex: medical & rehab expenses, funeral benefits, death benefits, loss of income benefits)
o No fault = payable by insured’s insurer regardless of fault
- Automobile property damage
o Subcoverage of automobile liability insurance
o Provides protection to insured against claim or suit for *damage to property of third party* due to operation of vehicle
- Collision
o Subcoverage of automobile physical damage coverage
o Protects insured in event of own fault (first-party coverage)
- Commercial Automobile Liability
o Protects from liability that arises from business use of owned, hired, or borrowed automobiles OR from operation of employee’s automobiles on behalf of the business insured.
- Crime Insurance
o Protects individuals & organizations from *loss of money*, *securities*, or *inventory* (due to crime)
o Ex: employee dishonesty, embezzlement, forgery, robbery, safe burglary, computer fraud, wire transfer fraud, counterfeiting
- Direct Compensation
o Insured collects directly from insurer, not from person who caused accident
o Only if other party is at fault
o Canada
- General Liability
o Wide array of insurance products
o (Ex. Premises, operations, products, completed operations, professional)
- Medical Malpractice
o AKA “medical professional liability insurance”
o Example in text drawn from old pivotal paper, “Loss Reserve Adequacy Testing: A Comprehensive, Systematic Approach” – Berquist & Sherman
- Personal Automobile Insurance
o AKA “private passenger automobile insurance”
o First-party and/or third-party coverages dependent on jurisdiction
- Primary Insurance
o First layer of insurance coverage
o Pays compensation for claims for insured event BEFORE any other coverages policyholder has
- Private Passenger Automobile Liability
o Protection against 3rdparty liability against claims/suits for bodily/property damage from operation of a private passenger automobile
- Private Passenger Automobile Physical Damage
o “Personal lines” coverage protecting against damage to or theft of covered private passenger automobile
- Property Insurance
o Protects against most risks (fire, theft, weather)
o Fire, flood, earthquake, home, boiler, machinery
- Umbrella & Excess Insurance
o Protects against claims above & beyond amounts covered by primary insurance policies, and sometimes for claims not covered by primary policies
- U.S. Workers Compensation
o “Workers Compensation and Employers Liability Insurance”
o Coverage for insured employer against benefits legally obligated to workers affected by workplace injury, illness, or disease
o Covers cost to defend against and amounts to be paid on account of bodily injury
Reserves:
Components of Unpaid Claims Estimate
- Case O/S (case outstanding)
- IBNER (incurred but not enough reported, aka development on known claims)
- Re-Opened
- IBNYR (pure IBNR)
- In Transit (reported but not recorded; soon to be logged)
Reported Claims
- Incurred claims/losses (does not include IBNR)
- Generally refers to *sum of cumulative paid claims* and *case outstanding estimates at a particular time*
Ultimate Claims
- Total dollar value after all claims are settled and closed with no chance of reopened claims
o Short-tail lines of insurance (property / auto physical damage)
§ Often know ultimate claims within 1~2 years
o Long-tail lines of insurance (U.S. general liability workers compensation)
§ Sometimes takes years or decades until value of ultimate claims are known
Actuarial Estimation Process
1. Project value of ultimate claims
2. Calculate estimate of unpaid claims for IBNR (& total unpair claim estimate = sum of IBNR + case outstanding)
3. Use projected ultimate claims for evaluating & selecting final unpaid claim estimate & determining accuracy of prior estimate of unpaid claims
“Claim-Related Expenses”
- More commonly known as total “loss adjustment expenses (LAE)” = ALAE + ULAE = DCC + A&O
“Experience Period”
- Domain of years/time included in specific technique for estimating unpaid claims
“Emergence”
- Rate of payment of ultimate claims
- Reporting/development of claims & claim counts over time
Chapter 2
The Claims Process
Information Extraction from a Claim:
- Effective dates of the policy
- Date of occurrence
- Terms & conditions of the policy
- Policy exclusions
- Policy endorsements
- Policy limits
- Deductibles
- Reinsurance or excess coverage
- Reporting requirements
- Mitigation of loss requirements
- Extent of injury and damages
- Extent of fault
- Potential other parties at fault
- Potential other sources of recovery
Initial case outstanding is created if covered, qualified incident/liability.
- Estimate value based on known info
- Methods:
o Best (arbitrary) estimate
o Maximum value (of policy)
o Seek advice of legal counsel (mode; mean/expected value)
- Case: Salvage & subrogation recoveries
o Some use estimate of salvage & subrogation recoveries that the insurer expects to receive to set up specific case outstanding
o Some track actual data of salvage & subrogation recoveries, but do not create case outstanding
Life of a Claim (Transactions)
- Establishment of initial Case O/S estimate
- Notification to reinsurer if claim expected to exceed insurer’s retention
- Partial claim payment to injured party
- Expense payment for independent adjuster
- Change in Case O/S estimate
- Claim payment (assumed to be final payment)
- Takedown of Case O/S & closure of claim
- [and possibly…]
- Reopening of claim & establishment of new Case O/S estimate
- Partial payment for defense litigation
- Final claim payment
- Final payment for defense litigation
- Closure of claim
Dates/Timeline of a Claim
- Policy effective date – insurer issues insurance policy
- Accident date (date of loss) – covered injury occurs
- Report date – insurer receives notice of claim
- Transaction date(s) – Case O/S transaction takes place, or payment made
- Closing dates – initially closed, then finally closed
- Reopening date – insurer reopens claim
[Reported Claims] = [Reported Claims @ end of period] – [Reported Claims @ beginning of period]
= (Paid claims during period) + [ (Case O/S @ end of period) – (Case O/S @ beginning of period) ]
= sum of cumulative claim payments through a specific date and the case outstanding at the same given date
Note that some analysts keep “cumulative paid claims” versus “incremental paid claims”
- Cumulative paid claims: sum of all claim payments through/up to given valuation date (0 -> t)
- Incremental paid claims: sum of all claim payments during given time interval
Part 2 – Information Gathering
Chapter 3
Understanding the Types of Data Used in the Estimation of Unpaid Claims
4-Step Process of Estimating Unpaid Claims
- Explore data for key characteristics and any possible anomalies. Also balance data with other verified sources
- Apply appropriate techniques for estimating unpaid claims
- Evaluate conflicting results & attempt to reconcile or explain different outcomes. Projected ultimate amounts are evaluated in context outside their original analysis frame
- Monitoring projections of claim development over time & compare projected and actual development of counts or amounts. One of the most useful diagnostic tools in evaluating accuracy of unpaid claim estimates.
TPA – Third Party Claims Administrators
- Handles claims beginning to end; contract for entire book of business
IA – Independent Adjuster
- Extra help or specific/specialized help; contract/compensation per individual claim
Homogeneity & Credibility of Data
- External data might not be relevant due to differences in practices / tendencies / styles / products
- Homogeneity – don’t pull together data from different lines of insurance (i.e. policies sold to corporations vs those for individuals; differences between subcoverage characteristics can be significant)
Key Actuarial Characteristics
- Consistency of coverage (generally subject to same/similar laws, policy terms, claims handling, etc)
- Volume of claim counts in the group
- Length of time to report claim after incident
- Ability to develop case outstanding in all stages of claim’s life
- Length of time to settle claim after reported
- Likelihood of claim to reopen once settled
- Average settlement value (severity)
Actuaries tend to group claims by lines & sublines of business that display similar traits in the above characteristics. They may group claims by policy limits to achieve similar claims attributes within a block of business.
Recoveries:
- Deductibles (third party line of insurance, pay injured full now, seek deductible back later from the insured)
- Salvage (Amounts insurer collects for sale of the damaged property)
- Subrogation (Insurer’s right to recover amount of claim payment to covered insured from third party responsible for injury or damage)
Reinsurance – NAIC outlines requirement for actuary to understand reinsurance & provide “relevant comment” paragraphs to address:
- Retroactive reinsurance
- Financial reinsurance
- Reinsurance collectability
- Capability or willingness of reinsurer to pay claims
Before commenting:
- Solicit information from management about any actual collectability problems
- Review ratings on reinsurers (given by recognized rating services)
- Examine schedule F for current year for indication of regulatory action or reinsurance recoverable on paid losses over 90 days past due
Exposure Data
- Some estimation techniques require measure of insurer’s exposure to claims
- Mainly use earned premium as exposure
- Otherwise, examples:
Lines of Insurance -> Exposure
- US Workers Compensation -> Payroll
- Automobile Liability -> # of vehicles or miles driven
- General liability (public entities) -> Population, Operating Expenditures
- General liability (corporations) -> Sales, sq. ft
- Hospital Professional Liability -> Average # occupied beds, outpatient visits
- Property -> Property value
- Crime -> # employees
Data Aggregation:
**Calendar Year (CY)
[CY EP] = [EP] + [ (beginning unearned premium reserve) – (ending unearned premium reserve) ]
Advantages (+)
- Compared to accident year, policy year, report year, (premium) values from CY remain fixed
- Readily available by usual financial reporting habits
- Useful for short-tail LOB like auto physical damage
Disadvantages (-)
- Fixed values -> inability to address the critical issue of development
- Worst match of loss & exposure (current year premium óother year losses)
**Accident Year (AY)
Can start on any date and have duration 1 year (fiscal year)
Advantages (+)
- Usable / applicable / “reliably estimable” SOONER than policy year & underwriting year
- Valuable to track when there are changes from economy or regulation (inflation or law reform) or major catastrophic events
Disadvantages (-)
- Potential mismatch between claims & exposures for insurers
- Includes claims from policies underwritten & priced at more varied times than policy or underwriting year aggregation
- High deductibles mask changes in retention
**Policy/Underwriting Year (PY/UY)
Policy year = year that the policy was written
Underwriting year (reinsurance only) = year reinsurance policy became effective)
Accident and occurrence dates for claims can spill over end of PY/UY for the policy duration
Advantages (+)
- True match between claims and exposures (e.g. premium)
- Particularly useful when only one policy may apply
- Very important for large pricing/underwriting changes:
o Shift: full coverage -> large deductible
o New emphasis on certain classes of business
o Increase/decrease in price charged (change in expected loss ratios)
o Change in type of policyholder insured
Disadvantages (-)
- Extended time frame -> longer time until data is complete / reliably estimable
- Difficult to isolate & understand the effect of particular event (catastrophe or major court ruling)
**Report Year (RY)
Coverage may be dependent on date reported (claim reported to insurer) (i.e. claims-made coverage -> use RY)
Lines of Insurance
- Medical malpractice
- Products liability
- Errors & omission
- Directors’ & officers’ liability
Advantages (+)
- Claim counts fixed at close of year (unique feature to this aggregation method) => more stable for successive use
- Useful for testing case adequacy over time
- Useful for claims-made policies (common in professional lines)
Disadvantages (-)
- Only measure development on known claims
- Cannot be used for IBNYR
Key Diagnostic Triangles
- Paid : Reported losses
- Closed counts : Total counts
- Closed w/ Payment Count : Reported Count
- (CNP) Closed No Payment Count : Reported Count
- Average Case O/S
- Average Paid on Closed
- Average Paid
- Average Reported
- Paid LAE : Paid Losses
- Reported LAE : Reported Losses
- Reported Losses : EP
- Reported Losses : OL EP
- Paid Losses : EP
- Paid Losses : OL EP
Noticeable/Materialized Changes via Triangles & Diagnostics
- Speedup or Slowdown in settlement rate
- Strengthening or weakening of case o/s
- Improvement or deterioration of u/w results
- (focus on closing small claims) vs (attention on large claims)
- New IT system: initial slowdown -> later speedup
- CAT occurrences overwhelming staff -> slowdowns
Chapter 7 – Development Technique
Assumes that past is indicative of the future (claims recorded to date will continue to develop in a similar manner in the future)
Also assumes:
- Consistent claim processing
- Stable mix of types of claims
- Stable policy limits
- Stable reinsurance (or excess insurance) retention limits throughout experience period
Steps/Mechanics (OVERVIEW)
1- Compile claims data -> Dev. Triangle
2- Calculate age-to-age factors
3- Calculate averages of age-to-age factors
4- Select claim development factors
5- Select tail factor
6- Calculate cumulative claim development factors
7- Project ultimate claims
Appropriate when:
- No major organizational changes
- No major environmental changes
- High frequency, low severity LOB w/ stable equally spaced claims throughout (AY, PY, RY, etc)
NOT appropriate after:
- New IT system
- Revisions to formulae for case o/s
- Changes in management philosophy, policyholder deductibles, reinsurance limits
- Major tort reform (historical data not indicative of future)
Chapter 8 – Expected Claims Technique
Often used for new LOB or new territories. Assumes it is better to use “a priori” (initial) estimate rather than observed experience
(Projected expected claims) = (predetermined exposure base) x (selected measure of claims per unit of exposure)
, where “selected measure of claims per unit of exposure” is “loss rate” or “pure premium”
(unpaid claim estimate) = (projected expected claims) – (paid claims)
Commercial insurers & reinsurers:
- Exposure base -> EP
- Measurement of claims -> claim ratio
- Therefore, expected claims = EP x Claim Ratio
Advantage (+)
- Stable over time (actual claims do not enter into the calculations)
- Ultimate claims only change if exposures / claim ratio / PP change
Disadvantage (-)
- Lack of responsiveness to recent experience
- Not responsive when actual claims differ from initial expectations
Chapter 9 – Bornhuetter-Ferguson Technique
Blend of prior two (development & expected claims) techniques. Especially used for long-tailed LOI, particularly for immature years. Splits ultimate claims into two components:
(actual reported claims) + (expected unreported claims)
OR
(paid claims) + (unpaid claims)
More weight is given to actual & paid claims as experience matures ; weight = Z
- Development method (full credibility Z = 1 given to actual claims experience)
- Expected Claims method (no credbility Z = 0 given to actual claims experience)
Credibility = % of claims developed @ particular stage of CDF (i.e. Z = 1.00/CDF)
Reported:
(Ultimate Claims) = (Actual Reported Claims) + (Expected Unreported Claims)
= (Actual Reported Claims) + (Expected Claims) x (% Unreported)
Paid:
(Ultimate Claims) = (Actual Paid Claims) + (Expected Unpaid Claims)
= (Actual Paid Claims) + (Expected Claims) x (% Unpaid)
(% Unreported) = 1.00 – 1/CDF
Advantages (+)
- Random fluctuations early in AY do not significantly distort projections
- Can be used even if not enough credible data (volatile and/or thin data)
- “expected loss ratio should be predictable enough [in stable and volatile lines] so that both tech’s produce the same result” [Bornhuetter-Ferguson vs. Expected Claims]
- Mostly used for long-tail LOB, but can be used for very-short-tail LOBs
- IBNR = multiple of last few months’ EP
Disadvantages (-)
- Bounds (Z in [0,1] ; CDF >= 1 ) can be an unrealistic assumption
- If uncredible data, heavily dependent on actuary’s judgement
Benktanker Method (modified Bornhuetter-Ferguson)
- Differs in derivation of expected claims
- “Iterative”B-F method
- Expected claims in Benktanker are the projected ultimate claims from BF projection
Benktanker proved mathematically that the projection of ultimate claims will approach projected ultimate claims produced by development technique after sufficient iterations
Benktanker gives greater credibility to dev. Tech., so more responsive than B-F
- Responsive to change in claim ratio
- BUT NOT responsive to changes in underlying development patterns (use other estimation techniques)
Chapter 10 – Cape Cod Technique (AKA) Stanard-Buhlmann method (SB)
Fundamentally similar to B-F method, but differs in *derivation of expected claims ratio*
Expected loss ratio
— obtained from reported claims experience (as opposed to independent/arbitrary/judgmental selection in B-F)
Assumes development of unreported claims is based on expected claims (similar to B-F), (not based on actual reported claims as is the case in Dev Tech).
Common/Applicable Uses:
- Reinsurance
- Usually reported claims but can be for paid claims
- Both short-tail & long-tail LOI
- AY, PY/UY, RY, FY ; monthly, quarterly, semiannual
(Ultimate Claims) = (Actual Reported Claims) + (Expected Unreported Claims)
(Expected Unreported Claims) = (Expected Claims) x (% Unreported)
When lacking historical rate level changes, rely on unadjusted earned premium data.
“used-up premium”
- Denominator in determination of expected claim ratio
- Corresponding to the claims that are expected to be reported through valuation date
- = ( EP ) x ( % Reported )
(Estimated Claim Ratios) = (Actual Reported Claims) / (Used-Up Premium)
Applicability:
- Similar to B-F, except if insufficient volume of credible reported claims (reliable expected claims estimate requires reliable input reported claims data)
- Ideally, use history of rate level changes to adjust historical premiums to on-level basis
- Also adjust claims for trend, benefit-level changes, & other similar factors
- Usually don’t have required info; continue without adjustment
- When selecting final ultimate claims values, acknowledge where assumptions might not be realistic
Chapter 11 – Frequency-Severity Techniques
Useful for:
- Additional estimates of unpaid claims
- Understanding drivers in claims activity
Simplest form (frequency – severity):
Frequency
- (Estimated Ultimate Number of Claims)
Severity
- (Estimated Ultimate Average Value)
Examine trends & patterns in:
- Reporting: rates of claims emergence
- Closure: settlement
- Average values of claims
Useful when insurer changes management, operations, or philosophy. Helps actuaries decide: accept or reject projection techniques.
3 Examples of Frequency-Severity:
- Development technique applied separately to claim counts (frequency) & average values (severity)
- Projecting ultimate claims for most recent 2 AY (Incorporation of Exposures & Inflation)
- Disposal rate analysis – rate of claim count closure at each maturity age & incremental paid severity by maturity age
(Examples of these triangles are done in Friedland)
Advantages (+)
- Usually the number of claims reported is stable -> development of ultimate claim counts gives reliable estimates
- Trend factors -> adjustments (“trended claim counts & severities”)
- Readily develop severity estimates for most recent AY
- Can use paid claims data, independent of Case O/S (not affected in change in Case O/S philosophy)
- Ability to explicitly reflect inflation (instead of assuming inherent trend accounts for inflationary forces)
Disadvantages (-)
- Estimate of unpaid claims is HIGHLY SENSITIVE to inflation assumption (incorrect inflation assumption -> incorrect unpaid claims estimate)
- Unavailability of required data
- Changes in definitions (claim counts, claims processing, or both) invalidate assumption that historical data are predictive of future development
Seasonality
- Tendency for claims to be asymmetric across time periods (i.e. more crashes around holiday seasons)
Inflation
- As discusses earlier in section, inflation affects both frequency & severity. To solve this, use more sophisticated methods than the 3 discussed here.