Briefly describe the six components of a reinsurer’s loss reserve
- Case reserves reported by the ceding companies • Reported on an individual claim basis (excess contracts) or in bulk summary form (proportional contracts)
- Reinsurer additional reserves on individual claims • Reinsurer reviews individual claims and specifies additional case reserves if necessary
- Actuarial estimate of future development on components 1 and 2 • Known as IBNER (incurred but not enough reserved)
- Actuarial estimate of pure IBNR • Usually combined with component 3 due to limitations in data systems. Together, components 3 and 4 are known as IBNR
- Discount for future investment income • Companies can take credit for future investment income on assets supporting certain types of claims, such as WC permanent total cases, auto PIP annuity claims and medical professional liability claims
- Risk load • Adverse deviation loading is used to keep reserves at a conservative level
Identify the three steps involved in reinsurer loss reserving.
- Partition the reinsurance portfolio into reasonably homogeneous exposure groups that are relatively consistent over time with respect to mix of business
- Analyze the historical development patterns. If possible, consider individual case reserve development and the emergence of IBNR claims separately
- Estimate the future development. If possible, estimate the bulk reserves for IBNER and pure IBNR separately
Define claim report lag R(t) in terms of the standard chain-ladder age-to-ultimate development factor.
The claim report lag at time t is the inverse of the chain-ladder age-to-ultimate development factor
Explain how the claim report lag can be interpreted as a probability cumulative distribution function. Give one reason why this interpretation is useful.
The claim report lag can be read as the probability that any particular claims dollar will be reported to the reinsurer by time t. This view allows us to compute statistics of the claims reporting process, enabling us to compare one claim report pattern with another
Given the following exposure types: Short-tailed exposures, Medium-tailed exposures, Long-tailed exposures
a) Identify one loss reserve estimation method for each exposure type above.
b) Provide two examples of each exposure type above.
a) Short-tailed – set IBNR equal to some percentage of the latest-year earned premium. Medium-tailed – chain-ladder method Long-tailed – Cape Cod method
b) Short-tailed – treaty property proportional, treaty property catastrophe Medium-tailed – treaty property excess higher layers, construction risk Long-tailed – treaty casualty excess, asbestos
Patrik describes a credibility procedure that weights the chain-ladder IBNR with the Stanard- Bu ̈hlmann IBNR. Briefly explain the rationale behind this procedure.
Due to the di culty in obtaining rate-level adjusted premium, we may not have complete confidence in the Stanard-Bu ̈hlmann approach. Thus, we can weight the chain-ladder and Stanard-Bu ̈hlmann methods together using a credibility factor
Patrik describes a credibility procedure that weights the chain-ladder IBNR with the Stanard- Bu ̈hlmann IBNR. Describe two alternative credibility procedures.
1) Weight together IBNR estimates based on reported claims and paid claims. The weights could be based on relative claim report and payment lags for each year
2) Use the ELR inherent in the underlying pricing of the exposure in lieu of or in conjunction with the Stanard-Bu ̈hlmann ELR. This ELR can be used to calculate BF IBNR. We then weight this BF IBNR with the chain-ladder IBNR
Describe three reasons why claim report lags for reinsurer tend to be longer then for primary insurers.
- Longer reporting pipeline
- Lengthened by undervaluation of serious claims by cedant
- Some mass tort claims have extreme delays in discovery (loss dates may be decided by courts)
Describe two reasons why reported losses for reinsurer generally develop more than for primary insurers after the claims have been reported
- Tendency to under reserve allocated loss adjustment expenses. Thus, the ultimate loss is understated
- Claims adjusters tend to reserve at modal values. Thus claims may not immediately pierce the attachment point of the reinsurance treaty
Briefly describe three reasons why many standard actuarial loss Development methods used by primary insurers may not work as well for reinsurer
Exposures assumed by reinsurance crossbows companies tend to be heterogeneous. Problem when typical reserving methods require homogeneous data. Low claim frequencies and long report lags cause extreme fluctuation in historical data Reinsurer know much less about specific exposures being covered than a primary carrier
Briefly describe two reasons why industry loss development statistics may not be useful for estimating loss development patterns for a reinsurer.
Information is much less specific Longer claim report
Describe four aspects of reinsurance loss reserving that make it somewhat more difficult than primary loss reserving.
1. Longer development pattern
2. Consistent upward development
3. Industry data not helpful
4. Claim Development is extremely different due to unique reinsurance contracts, significant fluctuation during development due to single large claims
Discuss two problems that may affect the accuracy of a reinsurer's earned premium data
1. Since the reinsurer relies on the insurer to report premium there is often a lag in reporting
2. Since earned premium is often reported I aggregate to the reinsurer, the reinsurer must make assumptions to split the premium by line of business