Werner ch 6

Sum of paid loss and ending case reserve

Reported Losses = Paid Losses + Case Reserve

• Amount required to settle all claims for a defined group of policies
• Differs from reported loss due to IBNR and case adequacy (or IBNER)
• IBNER - incurred but not enough reported or development on known claims

Ultimate Losses = Reported Losses + IBNR Reserve + IBNER Reserve

• 1. Choice of relevant statistics
• 2. Data aggregation method
• 3. Period of time

• Claim related expenses that can directly be attributable to a specific claim
• E.g., legal fees for outside counsel hired to work on a specific claim

• Claim related expenses that cannot directly be attributable to a specic claim
• E.g., claims department salaries and rent

• CY paid losses include payments made on any claim during calendar year
• CY reported losses equal paid plus change in case reserves

• Losses grouped according to date of occurrence, regardless of when pol written or claim reported
• AY paid losses include all payments made on claims that occurred in that AY
• AY reported losses include all payments plus ending case reserves for claims occurred in AY
• Accident year losses can change in successive calendar years

• Group losses by year in which policy was written
• Directly matches premiums and claims from a block of policies
• Paid and reported loss calculated similar to AY
• Policy year losses can change in successive calendar years

• Group claims according to date of report to the insurer
• Claims-made coverage is dependent on the report date
• No IBNR

Measures the portion of each premium dollar needed to pay loss

• Projected Ultimate Loss and ALAE ratio:
• Ultimate Loss Projected to Future Level / Projected Earned Premium at CR

• To project to level expected when rates will be in effect
• 1. Extraordinary Losses
• 2. Changes in coverage or benefit levels
• 3. Loss Development
• 4. Loss Trend

• How to determine threshold at which losses should be capped?
• Often capped at basic limits
• Ideally should correspond to point at which inclusion causes volatility in rates

• Include as many losses as possible
• Minimize volatility in analysis

• Typically use average expected large loss calculated using many years of data
• Length of time depends on size of insurer and line of business
• Note - older data may be less relevant (e.g., changes in jury awards)

• Event whose losses are very large and very infrequent such that their inclusion in a normal rate review would severely distort the estimation of future expected losses
• E.g., hurricane, earthquakes, oil spills

• Generally used on events that happen with some regularity
• E.g., hail storms for auto physical damage
• If not treated separately, increase indicated rate need in years after events and understate needed rate in years without events

Should be selected based on both stability and responsiveness

• Generally used for projecting extremely sporadic, high severity events
• Stochastic models to estimate likelihood of events with varying magnitude
• Estimate damages resulting from events given characteristic of insured properties
• Catastrophe provision added to non-cat loss amount to get aggregate expected losses

• Reduce projected losses for reinsurance recoveries and premiums for cost of reinsurance
• Net cost of non-proportional reinsurance may be included as an expense item

Project unpaid (often unreported) claims to ultimate settlement values

• 1. Future claims' development is similar to prior years' development
• 2. Claims recorded to date will continue to develop in a similar manner in the future
• Past is indicative of the future

• 1. Step 1 - Compile loss data in a development triangle
• 2. Step 2 - Calculate age-to-age factors (a.k.a. report-to-report factors or link ratios)
• 3. Step 3 - Calculate averages of the age-to-age factors
• 4. Step 4 - Select loss development factors
• 5. Step 5 - Select tail factor
• 6. Step 6 - Calculate cumulative loss development factors
• 7. Step 7 - Project ultimate claims

• 1. Bornhuetter-Ferguson Method
• Unreported (or unpaid) claims will develop based on expected claims
• 2. Berquist-Sherman Method
• Deals with changes in claims settlement rates or case reserving philosophy

Adjust data for changes in frequency and severity

• Monetary inflation
• Increasing medical costs
• Advancements in safety technology
• Distributional changes in the book of business
• Social Iflnuences, such as changes in claim consciousness, court practices, legal precedents

Period of time from average loss occurrence date of experience period (usually cal/acc year) to average loss occurrence date for period in which rates will be in effect (usually policy year)

• Used when expect trend in historical period and forecast period to be dffierent
• Legislative changes
• 1. Trend losses from average occurrence in experience period to average accident date in last data point in trend data
• 2. Trend from average accident date of last data point to average accident in forecast period

• Assuming a constant percentage trend acting on all sizes of loss
• Basic limit losses will trend at a lower rate than losses limited at higher limits
• Which in turn trend at a lower rate than excess layers

• 1. Has been incorrectly suggested that severity trend is double counted when both loss development factors and severity trend factors applied to losses
• 2. Both necessary
• Trend factor reflects trend between midpoint of experience period and midpoint of exposure period
• The LDF reflects trend between occurrence and settlement