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102 Cards in this Set
- Front
- Back
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Life vs. Casualty Ratemaking
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1. Cancellation - P/C carrier has right to terminate the policy at renewal
2. Claim Costs - vary by duration in life/health more so than P/C 3. Expenses - show similar pattern, one difference is first year commission for life is high, but low for renewals; for P/C independent agents commissions do not differ between years 4. Level premiums - common in life insurance; P/C rates may be revised each year |
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Developments in Casualty Insurance
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1. Commissions: personal direct writers have higher first year commission rates
2. Cancellations - rarely cancels contracts; want stability in book of business 3. Loss costs - expected loss costs are greater for new business than renewal |
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Asset share pricing is not yet common in P/C insurance
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1. Data needed are not always available
2. Casualty pricing techniques do not always take into account long-term profit considerations 3. The casualty insurance policy allows greater flexibility in premiums and benefit levels 4. Liability claim costs are uncertain, both in magnitude and timing |
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Fundamental issue of asset share pricing
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the relationship of losses and expenses to persistency
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Relationship between duration of the policy and expected claim frequency results from:
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1. Experience - good driving habits acquired over time
2. Youth - young drivers have higher than average claim frequencies; have relatively new policies 3. Transcience - many high risk drivers, such as young males, have high termination rates a. Young males are more likely to voluntarily cancel their policies b. Underwriters are more likely to cancel a young male driver than an adult c. Young males are more likely to experience financial difficulties or not pay premiums d. Young males with high premiums have more incentive to shop around 4. Acquisition of the Vehicle - insured not familiar with car 5. D'Arcy's four a. Inability to surcharge new insureds properly since less information is available b. Higher loss potential of insurance shoppers who switched around looking for bargain coverage c. New insureds include a high proportion of risks not wanted by other insurers d. New insureds may be individuals unfamiliar with local driving conditions |
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Crux of asset share pricing
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Persistency rates or retention rates
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P/C expense costs are greater in the original year of issue because...
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a. Underwriting expenses -incurred predominantly in the first year include salaries, cost of policy issuance, and underwriting reports
b. Loss control expenses - incurred at or before policy issuance include technical inspections, landfill inspections, loss engineering services, financial analysis, and building inspections c. Acquisition expenses - for direct writers are greater in the first year; three types of commission schedules used in P/C insurance 1) Independent agency companies pay level commissions - agent owns renewals and would move business if lower commission on renewal, level commission does not reflect actual incidence of expenses 2) many direct writers pay commissions that vary by policy year 3) some direct writers have either a salaried sales force or a sales force that is compensated partly by commission and partly by salary d. most "other acquisition expenses" such as advertising, subsidies for new agents, and development costs are expended at or before the inc |
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Termination Rate
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number of terminations during a given renewal period divided by the sum of terminations during that period plus policies persisting through that period
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Probability of Termination
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number of terminations during a given renewal period divided by the number of originally issued policies in that cohort
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Persistency rate
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1-termination rate
the proportion of business that remains in force from one period to the next. |
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How might traditional ratemaking methods be misleading in determining classification relativities?
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Traditional ratemaking methods use loss cost relativities instead of rate relativities. The main reason is the rate relativity is different from the loss cost relativity is persistency. Loss cost relativities do not consider persistency rates, they tend to underestimate relativities for classes with poor persistency and overestimate relativities for classes with good persistency
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How do asset share pricing models and property/casualty insurance ratemaking methods differ in their consideration of the profitability of an insurance policy
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Asset share pricing models examine the profitability of the complete insurance contract from inception to termination, including all renewals of the policy. P/C ratemaking methods only consider the next policy year
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What three viewpoints are affected by accurately estimating unpaid claims
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Internal Management - used for decision making, pricing, financial results -> drive decisions such as underwriting - increase business/exit market, strategic- reinsurance needs, financial - capital management
Investors-inaccurate reserves can cause misstated balance sheets and income statements, inaccurate reserves can lead to misleading financial metrics Regulators- rely on financial statements to supervise, inadequate reserves may result in misstatement of true financial position, may delay regulator intervention and not allow them to help insurer |
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Actuarial central estimate
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an estimate that represents an expected value over the range of reasonably possible outcomes
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Components of Unpaid Claim Estimates
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1. Case outstanding on known claims (estimate of unpaid established by claim department)
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) |
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2 components of IBNR
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1. Incurred but not yet reported (pure IBNR (4+5)
2. Incurred but not enough reported (IBNER 2+3) |
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Calendar Year Case Incurred Loss
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Paid claims during cal year + Ending case outstanding - Beginning case outstanding
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Accident Year Case Incurred
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Paid claims for all reported claims incurred in accident year + Ending case outstanding
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4 phase approach to the process of estimating unpaid claims
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1. Exploratory analysis of the data - identify key characteristics and possible anomalies, balancing data to other verified sources
2. Apply appropriate techniques for estimating unpaid claims 3. Evaluating the conflicting results of the various methods - attempt to reconcile or explain the different outcomes, projected ultimate amounts evaluated in contexts outside their original frame of analysis 4. monitoring projections of claim development over subsequent calendar periods - deviations of actual development from projected one of most useful diagnostic tools in evaluating the accuracy of unpaid claim estimates |
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Key characteristics for credible data
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1. consistency of coverage triggered by the claims in the group
2. volume of claim counts in group 3. ability to develop an appropriate case outstanding estimate from earliest report through the life of the claim 4. settlement or payment patterns 5. likelihood of claim reopening 6. severity |
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Credibility
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predictive value given to a group of data
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Salvage
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the amount an insurer gets by selling damage property acquired when paying claims
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Subrogation
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the recovery of claim paid by insurer from an at-fault third party
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Policy Effective Dates
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beginning and ending dates of the policy term
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Accident dates
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date on which the loss occurred
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Report date
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date on which the loss is first reported to an insurer
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Accounting date
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date used to define the group of claims to be included in the liability estimate
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valuation date
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date as of which the evaluation of the loss liability is made
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Aggregation by Calendar Year
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-transactional data
-premium: written - the sum of all written premium reported/recorded during CY, earned: written + beginning UEPR - ending UEPR adv - no future development - value remains fixed and doesn't change over time & readily available since used on most financial reporting disadv - inability to address the critical issue of development |
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Aggregation by Accident Year
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Claims are grouped according to date of occurrence,
Adv- grouping is easy to achieve and understand, represents claims occurring over a shorter time frame than py, numerous benchmarks available, tracking claims by AY valuable when there is change due to economic or regulatory forces Disadv- potential mismatch between claims and exposures, includes claims from policies underwritten and prices at more varied times than PY, for self-insureds with high deductibles, AY data can mask changes in retention levels and/or changes in insurers that could have an affect on claim development For self insurers- CY exposures represent and exact match with AY claims |
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Aggregation by Policy Year or Underwriting Year
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sort claims by year in which policy was writter. directly matches premiums and claims from a block of policies
Adv - true match between claims and exposures, PY experience can be very important when underwriting or pricing changes occur Disadv-extended time frame, difficult to understand and isolate affect of a single large event |
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Aggregation by Report Year
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group claims according to the date of report to the insurer
actuaries use to estimate the ultimate value of known claims adv- number of claims is fixed at close of year disadv-only measure development on known claims and not pure IBNR |
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Diagnostic Triangles used to figure out LR deterioriation
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Ratio of reported Claims to Earned Premium
Ratio of Reported Claims to On-Level Earned Premium |
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Diagnostic Triangles used to figure out Speed up of claims or change in case reserve
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Ratio of paid to Reported Claims
Ratio of Paid Claims to On-Level Earned Premium Ratio of Closed to Reported Claim Counts |
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Diagnostic Triangles used to figure out severities
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Average Reported Claim Development
Average Paid Claim Development Average Case Outstanding Development |
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Forces that could result in a change in ratio of closed to reported claim counts
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1) Large catastrophic storm has potential to temporarily limit insurer's operations
2) Change in guidelines for the establishment of a claim 3) Decrease in the statue of limitations which often accompanies major tort reforms 4) Delegation of a higher limit for settlement of claims to a TPA 5) Restructuring of the claim field offices such as merging offices or adding new ones 6) Introduction of a new call center to handle claims |
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Key Assumptions in Development Technique (Chain Ladder)
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1. Future claims' development is similar to prior years' development
2. Implicitly assumes claims observed for an immature AY tell you something about claims yet to be observed 3. Other important assumptions a) Consistent claims processing b) Stable mix of claims types c) Stable policy limits d) Stable reinsurance retention limits throughout experience period |
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Percentage Reported
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1/Cumulative CDF
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When development technique works and when it does not
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Does not:
-Changes in insurer's operations (assumption that the past will be predictive of the future may not hold) -insufficient volume of credible data -Highly leveraged factors results in projections that are very sensitive to current value of claims Works well: -Presence or absence of large claims does not greatly distort the data -Works well with high frequency, low severity lines with stable and timely reporting of claims |
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Influence of a Changing Environment on the Claim Develop Techniques: Steady State
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projected ultimate claims are the same for both reported and paid claim development
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Influence of a Changing Environment on the Claim Develop Techniques: Increasing Claim Ratios with No Change in Case Outstanding Strength
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Development technique is responsive to changes in underlying claim ratios assuming no changes in underlying claims reporting or payment pattern
Still estimates correctly (paid + reported) |
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Influence of a Changing Environment on the Claim Develop Techniques: Stable Claim Ratios with Increasing Case Outstanding Strength
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Reported claim development technique overstates the projected ultimate claims
Paid claim development technique will produce the correct estimate |
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Influence of a Changing Environment on the Claim Develop Techniques: Increasing Claim Ratios with Increasing Case Outstanding Strength
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Paid development produces the actual value for IBNR
Reported claim development overstates the estimate of underpaid claims due to changing case reserve adequacy |
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Approaches to determine a tail factor
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1. Use insurance industry benchmark data
2. Fit a curve using average or selected LDF exponential decay model |
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Expected Claims Technique Key Assumption
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Unpaid claims can better be estimated based on an a priori estimate than using experience to date
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Common Uses of the Expected Claims Method
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-used in lines with longer emergence and settlement patterns
often used when: -insurer enters a new line of business or new territory -operational or environmental changes make recent historical data irrelevant for projecting -claim development method is not appropriate for less mature periods due to highly leveraged development factors -data is unavailable for other methods |
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When Expected Claims Techniques and When It does not
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Used when:
-entering a new line of business or new territory (use insurance industry benchmarks for claim ratios, pure premiums, development) -when cumulative claim development factors are highly leveraged -when insurer has experienced significant change due to internal factors or external influences adv-maintain stability over time disadv- lack of responsiveness to recent expeirence |
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Influence of a Changing Environment on the Expected Claims Techniques: Steady-State
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Generates accurate estimate of IBNR
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Influence of a Changing Environment on the Expected Claims Techniques: Increasing Claim ratios with no change in case outstanding strength
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weakness of method is that it lacks responsiveness. increasing claim ratios will cause method to understate IBNR
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Influence of a Changing Environment on the Expected Claims Techniques: Stable Claim Ratios with Increasing Case Outstanding Strength
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adequacy of case outstanding have no effect on the expected claim ratio method, expected claims method produces an accurate estimate of IBNR
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Influence of a Changing Environment on the Expected Claims Techniques: Increasing Claim Ratios with Increasing Case Outstanding Strength
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Not affected by change in case, but affected by increasing claim ratios. Will understate IBNR
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Cape Code Technique (Standard Buhlmann)
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ECR is obtained from the reported claims experience rather than independent and judgmental selection as in BF. Unreported (or unpaid) claims will develop based on expected claims
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Common uses of cape cod technique
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1. Reinsurers are most frequent users. Generally used with reported claims, but can also use with paid claims.
2. Used for all lines of insurance 3. Works with many time intervals - AY, PY, UW Years, Rpt year, Fiscal yr 4. May organize data by year, half-year, quarter, or month |
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Cape Code (SB) ECR
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Sum of Reported Claims / Sum of (Adj EP*%Rpt)
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When the Cape Cod Technique Works and When it Does Not
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Adv - random fluctuations at early maturities do not significantly distort the projections
-Not appropriate as BF when data is extremely thin or volatile or both -Ideally, premiums are adjusted to an on-level basis and claims adjusted for trend, benefit level changes, and other similar factors |
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Influence of a Changing Environment on the Cape Cod: Steady-state
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Generates accurate estimate of IBNR in steady-state
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Influence of a Changing Environment on the Cape Cod: Increasing Claim Ratios with No Change in Case Outstanding Strength
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-Does not lack responsiveness like expected claims and BF techniques. ECR based on reported claims to date.
-Though it is more responsive than BF because of the increased ECR, the Cape Cod method still understates IBNR, but not by as much as EC or BF |
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Influence of a Changing Environment on the Cape Cod: Stable Claim Ratios with Increasing Case Outstanding Strength
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-Cape Cod method overstates the IBNR by more than BF
-Increases in reported CDFs lead to increases in %unrpt -Unlike BF, there is a change (increase) in the expected claims,w hich leads to the higher overstatement |
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Influence of a Changing Environment on the Cape Cod: Increasing Claim Ratios with Increasing Case Outstanding Strength
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Cape Cod has two factors working against each other
1) Increasing Claim Ratios causes Cape Cod to understate IBNR 2) Increasing case strength causes Cape Cod to overstate IBNR -difference from the actual IBNR using the Cape Cod could be positive or negative -Reserve adequacy depends on the mix of loss ratio and reserve adequacy changes, which offset each other |
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What happens if product mix is changed for Cape Cod?
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Cape Cod does not respond appropriately to the changing product mix
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Difference between the Cape Cod and BF
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The cape cod uses reported claims experience for the expected claim ratio. BF uses an independent and often judgmental selection. (BF method uses an a priori estimate of the claims ratio)
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Frequency Severity
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-provides additional estimates of unpaid claims, help in understanding the drivers in claim activities, project ultimate claims by mulitplying est ult number of claims by est ult avg value
Adv- can examine trends and patterns in claim emergence and settlement, and average values |
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Common Uses for Frequency Severity Techniques
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-Used with accident year, policy year, report year, and calendar year data
-appropriate for all lines of insurance (most often used with long-tailed lines, can be used for both primary and excess layers) |
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Key Assumptions: Freq-Sev - development technique with claim counts and severities
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-Consistent definition of claim counts over experience period
-Claim counts are reasonably homogeneous -Because it uses the development method, assumes claim counts to date will continue to develop in similar manner |
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Negative IBNR can result from
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Salvage and subrogation recoveries
Conservative case reserves |
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Key Assumptions of Freq-Sev Incorporation of Exposures and Inflation into Methodology
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-Claim counts and reported claim activity will continue to develop in similar manner
-Claim counts are defined consistently over time -Mix by claim type is reasonably consistent -Trend rates are used -> Selection of freq/sev trends often reflect economic and social inflation ->vary by line of business and even subcoverage within a line ->can be significant variation in trend rates for exposures, freq&sev by geographic region ->can vary based on limits |
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Key Assumption of Freq-Sev Disposal Rate Technique
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-Claim counts and reported claim activity will continue to develop in similar manner
-Claim counts are defined consistently over time -Mix by claim type is reasonably consistent |
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Disposal rate
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The AY cumulative closed claim count at a certain age divided by the selected ultimate AY claim count
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Formula to figure out claims disposed
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(disposal rate at y-disposal rate at y-12)/ (1-disposal rate at latest diagonal) * (Ult Clm Counts - Closed Claim counts to date)
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When Freq/Sev Works and When it Does Not
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Adv
-Gain greater insight into the claims process -may be used with paid claims data only -ability to explicitly reflect inflation in the projection DisAdv -Highly sensitive to the inflation assumption -Data needed may be unavailable -Changes in definition of claim counts or claims processing -Methods rely on mix of claims to be relatively consistent |
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Case Outstanding Development Technique: Key Assumptions
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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
Method is appropriate when applied to lines for which most claims reported in first accident period |
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When the Case Outstanding Development Technique Works and When it Does not
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Assumption that future IBNR is related to claims already reported does not hold true for many P&C lines, infrequently used and lack of benchmarks
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Case Outstanding Development Factor
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(Rpt CDFult - 1)* (Paid CFD ult) / (Paid CDF ult - Rpt CDF ult) + 1
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Substitute types or forms of data for Berquist-Sherman Technique
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a. Use earned exposure instead of claim counts
b. Substitute policy year for accident year when limits or deductible change in successive years c. Substitute report year for accident year when there has been a dramatic shift in the social or legal climate which causes claim severity to more closely correlate with the report date d. Substitute accident quarter for accident year when growth of earned exposures shifts avg accident date |
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Claim development diagnostic tests
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-ratio of paid to reported
-average case outstanding -average reported claim -average paid claim |
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Difficulties with Adjustment for B-S Method
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lack of recognition of settlement patterns by size of loss may increase error
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Advantage to selecting claims disposed ratios for the latest calendar year for B-S Method
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The most recent values of cumulative paid claims for each accident year remain unchanged. It eliminates the need for extrapolation into the future in making adjustments
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State and describe a problem that can be mitigated by analyzing claim experience by separate size of claim categories (B-S Method)
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1. Shifts in emphasis by the claims department on priorities in settling large vs. small claims - such a shift could cause major distortions int he claim projections of nearly all reserving methods.
2. Changes in the claims procedures for very small or trivial claims - when guidelines for the establishment of a claim file for very small claims are changed, may result in noticeable distortions in claim count data, and may adversely affect frequency and severity projections |
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What distortion does B-S Method fix?
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Change in claim settlement rate
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Possible sources of distortions in predicting future payments
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1. Change in claims procedures - slow down in claims closure
2. Catastrophic claims in experience - adjusters may have a backup of claims 3. Mix of property and liability claims - different settlement rates 4. Major changes in rate of growth of earned exposures - cause shift in average acc date 5. New type of claim emerges - may have different settlement pattern 6. Large claim - could adversely affect development |
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Two reasons why using paid claim data to estimate a severity trend can be inappropriate for medical malpractice claims
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1. Slowly paid out pattern reduces the available experience claim data
2. Irregular payment pattern and variation of the portion of claims closed without payment |
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Salvage
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Amount insurer is able to collect from sale of damaged property acquired when paying insured for a total loss
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Subrogation
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insurer's right to recover the amount of claim payment to a covered insured from a third-party responsible for the injury or damage
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Advantage of using the ratio approach for S&S recoveries
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the development factors tend not to be as highly leveraged
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Claims to Emerge in the Future Formula
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IBNR x (% rpt @ t+12m - % rpt @ 12m)/ (% unrept @12m)
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Reasons for reviewing unpaid claims between annual analyses
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1. It must be determined if changes in the unpaid claims are necessitated by changing exposures
2. The unpaid claims established at the prior year-end must be continuously monitored to see if the claim developments observed are what were contemplated when the unpaid claims established. To the extent that the actual development is different from the expected and credible, the unpaid claim structure should be fine-tuned |
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Assumption of Paid ALAE to Paid Claim Development
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-relationship between ALAE and claims is relatively stable over the experience period
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Ratio of Paid ALAE to Paid Claim Development Multiplicative Approach (Adv+ Disadv)
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Adv
-recognizes the relationship between ALAE and claims -ratio development factors tend not to be as highly leveraged -easy to interject actuarial judgment in projection analysis Disadv -Any error in estimate of ultimate claims could affect estimate of ultimate ALAE -For some lines, large amounts of ALAE may be spent on claims with no claim payment |
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Ratio of Paid ALAE to Paid Claim Development Additive Approach (Adv)
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Advantage over multiplicative approach - more stable approach when ratios are very small at early maturities
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Dollar Based ULAE method
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ULAE expenditures track with loss dollars
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Count based ULAE method
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same kind of transaction costs = the same amount of ULAE, despite claim size
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Assumptions of Classical or Traditional Technique (Paid to Paid Ratio Method) ULAE
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-Specific company's ULAE to claim relationship have achieved a steady state
-Relative volume and cost of future claims-management activity on unreported and open reported claims will be proportional to IBNR and case outstanding dollars -50% of the ULAE occurs when claim is reported, 50% when closed |
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Challenges of Classical Technique (ULAE)
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"Closing" and "paying" a claim may not mean the same thing
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Steps to Classical Technique
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1) Calculate historical CY paid ULAE to CY paid claims
2) Review historical paid ULAE to paid claims ratios for trends or patterns 3) Select ratio of ULAE to claims for future claims payments 4) Apply 50% of ratio to case outstanding and 100% to IBNR = Ratio* (50% Case OS + IBNR) |
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When the Classical Technique Works and When It Does Not
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Works:
-very short-tailed, stable lines of business -low cost inflation May Not Work: -Long- tail lines of business -Times of changing inflationary forces - past or expected future -Rapid change in volume |
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Kittel's Refinement to the Classical Method
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Explicitly recognizes fact that ULAE is incurred as claims are reported, even when no loss payments are made
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Key Assumptions of Kittel's Refinement
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-ULAE incurred with the reporting of claims, with or without payment
-ULAE payments during a calendar year are related to both reporting and payment of claims -Relative volume and cost of future claims-management activity on unreported and open reported claims will be proportional to IBNR and case outstanding dollars |
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Steps to Kittel Refinement
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1) Calculate historical CY Paid ULAE to average of CY Paid and CY incurred claims
2) Review historical ratios for trends or patterns 3) Select ratio of ULAE to claims for future claims payments 4) Apply 50% of ratio to case outstanding 100% to IBNR = Ratio*(50%Case OS + IBNR) |
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When Kittel Refinement Works and When it Does Not
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Works
-Can handle growing insurer situation that classical technique cannot May Not Work -maintains 50/50 assumption (does not allow particular allocation of ULAE to opening, maintaining, and closing) -times of changing inflationary forces |
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Assumtions Conger and Nolibos Method - Generalized Kittel Approach
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-Generalized method assumes expenditure of ULAE resources is proportional to dollars of claims being handled
-ULAE amounts spent opening claims are proportional to the ultimate cost of claims being reported -ULAE amounts spent maintaining claims are proportional to payments made -ULAE amounts spent closing claims are proportional to ultimate cost of claims being closed |
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Mango-Allen Refinement Assumptions
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ULAE to claim relationship is derived using paid ULAE to expected paid claims
Relative volume and cost of future claims-management activity on unreported and open reported claims will be proportional to IBNR and case outstanding dollars |
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When Mango-Allen Refinement Works and When It Does Not
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Works
-good option for insurers with limited experience, highly volatile claims payment experience Does Not Work -insurers with sufficient volume of paid claims experience |
