Patrik Flashcards
Briefly describe the six components of a reinsurer’s loss reserve.
⇧ Component 1: Case reserves reported by the ceding companies ⇧ Component 2: Reinsurer additional reserves on individual claims ⇧ Component 3: Actuarial estimate of future development on components 1 and 2 ⇧ Component 4: Actuarial estimate of pure IBNR components 3 and 4 are known as IBNR ⇧ Component 5: Discount for future investment income ⇧ Component 6: Risk load
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.
Part 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 Part 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-B¨uhlmann IBNR. a) Briefly explain the rationale behind this procedure.
Due to the difficulty in obtaining rate-level adjusted premium, we may not have complete confidence in the Stanard-B¨uhlmann approach. Thus, we can weight the chain-ladder and Stanard-B¨uhlmann methods together using a credibility factor
Patrik describes a credibility procedure that weights the chain-ladder IBNR with the Stanard-B¨uhlmann IBNR. b) Describe two alternative credibility procedures.
⇧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 ⇧Use the ELR inherent in the underlying pricing of the exposure in lieu of or in conjunction with the Stanard-B¨uhlmann ELR. This ELR can be used to calculate BF IBNR. We then weight this BF IBNR with the chain-ladder IBNR
7 Problems with Reinsurance Reserving
- Report Lag is Longer 2. Persistent Upward Development of Loss Reserves 3. Reporting Patterns are heterogenous 4. Industry Statistics not useful because of heterogeneity 5. Reports Lack Important Information 6. Data Coding and IT systems problems 7. Loss Reserves to Surplus is high
6 Components of a loss reserve
- Case Reserves 2. Additional Case Reserves 3. Development on Known Claims (IBNER) 4. Pure IBNR 5. Discount (where permitted) 6. Risk Load
When Reserving for Reinsurance, what variables should we partition across?
-Line of Business -Type of Contract (Facultative, Treaty, Finite) -Type of Cover (Quota, Surplus, XOL, Aggreggate Excess, Catastrophe, LPT) -Primary LOB (for Casualty) -Attachment Point (for Casualty) -Contract Terms (Flat Rate, Retro, Sunset Clause, Share of LAE, Claims Made) -Type of Cedant (small, large, E&S company) -Intermediary
What Methods to use when Reserving Medium-Tailed Lines
Can use Paid or Incurred Method Can use Additional Case Reserves
What Methods to use to when Reserving Long-Tailed Lines
A Bornhuetter-Ferguson Approach is better than Chainladder Stanard-Buhlmann (Cape Cod)
Credibility formula for estimating Long-Tail Reserves
Stanard Buhlmann Method for Setting Reserves
