Patrik

Question 1

Reinsurance Loss Reserving Problems

Answer 1

1. Claim report lags to reinsurers are generally longer, especially for casualty excess losses
2. There is a persistent upward development of most claim reserves
3. Claims reporting patterns differ greatly by reinsurance line, by type of contract, by specific contract terms, by cedant and possibly by intermediary
4. Because of the heterogeneity stated in Problem 3, industry stats are not very useful
5. The reports the reinsurer receives may be lacking important information
6. Because of the heterogeneity in coverage and reporting requirements, reinsurers often ahve data coding and IT problems
7. The size of an adequate loss reserve compared to surplus is greater for a reinsurer

Question 2

Components of a Reinsurers Loss Reserves

Answer 2

1. Case reserves reported by the ceding companies (excess-individual, proportional-bulk)
2. Reinsurer additional reserves on individual claims. (Reviews individual claims and specifies additional if needed)
3. Actuarial estimate of future development on components 1 and 2 (IBNER)
4. Actuarial estimate of pure IBNR
5. Discount for future investment income (certain types of claims such as PIP or WC)
6. Risk Load (Adverse deviation loading is used to keep reserves at a conservative level, some actuaries load this in implicity through conservative assumptions, while others account for it explicity)

Question 3

Steps in Setting Reinsurance Loss Reserve

Answer 3

1. Partition the reinsurance portfolio into reasonably homogenous exposure groups that are relatively consistent over time with respect to mix of business. (LOB, Contract type, Reinsurance cover, attachement point, intermediary)
2. Analyze the historical development patters. If possible, consider individual case reserve development and the emergence iof IBNR claims separately.
3. Estimate the future development. If possible, estimate the bulk reserves for IBNER and pure IBNR separately. (patterns over long period times. Do in 3rd/4th quarter)
4. Monitor and test predictions

Question 4

Reinsurance Reserving Problem #1

Longer Report Lags

Answer 4

1. Claim must first be perceived as reportable
2. Claim must filter through:
   - Cedant’s reporting system
   - Cedant’s reinsurance accounting
   - An intermediary
   - Reinsurer books the claim
   - Makes its way to reinurers claim system
3. Cedant may undervalue the claim
4. Extreme delays in mass torts

Question 5

Reinsurance Reserving Problem #2

Persistent upward develop of reserves

Answer 5

1. Economic and social inflation
2. Tendency to underestimate the loss adjustment expenses
3. Tendency of claims to be reserved at modal value (most popular)

Question 6

Reinsurance Reserving Problem #3

Reporting Patterns not Homogenous

Answer 6

1. Assumed exposure is heterogeneous-reserving methods assume homogeneity
2. Volatile data due to low frequency, long reporting lags
3. Reinsurer know much less about exposure than primary

Question 7

Reinsurance Reserving Problem #4

Industry Statistics Unhelpful

Answer 7

1. Schedule P is not comparable across reinsurers
2. ISO development stats not directly applicable
3. Heterogeneity of profile
4. Every 2 years Reinsurance Association of America publishes summary of casualty excess reinsurance loss development statistics
5. Most reinsurers’ loss reserves are aggregated into one LOB

Question 8

Reinsurance Reserving Problem #5

Reports are Lacking Important Info

Answer 8

1. Proportional covers require only summary info.
2. May only have UW Year or Calendar Year.
3. For most treaties, premium and losses are reported quarterly, in arrears. Thus, always missing a quarter of premium.
4. It’s desirable to have a professional reinsurance claims staff to advise cedant’s staff.
5. In loss reserving, it’s useful to have an exposure measure to compare loss estimates against.
6. For most treaties, there tends to be an added IBNR exposure for both premiums losses.

Question 9

Reinsurance Reserving Problem #6

Data Coding and IT Systems Problems

Answer 9

1. Business has grown in size and complexity faster than data systems could handle
2. Heterogeneity in coverage and reporting requirements

Question 10

Resinsurance Reserving Problem #7

Adequate Loss Reserve Large Compared to Surplus

Answer 10

1. Management problem (as opposed to technical)
2. Actuary may struggle in convincing management to post the appropriate reserve
3. US Tax Reform Act of 1986

Question 11

U.S. Tax Reform Act of 1986

Answer 11

1. Requires the discounting of loss reserves for income tax purposes.
2. Now that insurers must discount loss reserves, they no longer have an implicit risk margin built into their loss reserve estimates.
3. This buffer flows into profits and is taxed sooner, decreasing assets and increasing companies’ risk level

Question 12

Claim Report and Payment Lags

Answer 12

• When analyzing patterns, look at the inverse of the chain-ladder development factors. (lags)
• Create a graph with time on x-axis and lag percentage on y-axis
• Graph resembles a probability cdf and can be interpreted as probability that a particualr claims dollar will be reported ot the reinsurer by time t
• Stats can be calculated from this curve

Question 13

Methods for Short-Tailed Exposure Categories

Answer 13

• Exposure for which losses are reproted and settled quickly
• Treaty prop proportional, treaty prop catastrophe, treaty prop excess, facultative property
• Method 1: Set IBNR equal to some percentage of the latest year EP
• Method 2: Reserve up to a selected loss ratio (good for new LOBs), where the selected loss ratio is larger than the one computed from reported non-cat claims
• If losses summarized by UW year, then percentage estimates should be used to allocate losses to true accident years to avoid overstating AY loss development

Question 14

Methods for Medium-Tailed Exposure Categories

Answer 14

• Any exposure for which claims are almost completely settled w/in 5 years and with avg agg claims dollar report lag of one to two years
• Consists of Treaty prop excess higher layers, construction risks, surety
• Method 1: Standard CL Method
  
  • Advantage is that it strongly correlates future development with an overall lag pattern
  • Disadvantage is that IBNR is so correlated with reported claims that estimates not very credible for recent immature years
  • Can use pd instead of reported to increase stability

Question 15

Method for Long-Tailed Exposure Categories

Answer 15

• Any exposure for which avg agg claims dollar report lag is over two years and whose claims are not settled for many years
• Consists of Treaty casualty excess, treaty casualty proportional, asbestos, pollution
• Asbestos, pollution, mass tort analyzed separately
  
  • No claims for long time periods followed by huge
  • Cannot use traditional reserving methods
  • Must rely on complex models
• Method 1: Standard CL method
• Method 2: BF method
  
  • correlates to future development for each year
  • dependent on selected LR is disadvantage
• Method 3: Stanard Buhlmann (Cape Cod)
  
  • Key innovation is that the ultimate ELR for all years combined is estimated from overall rptd claims experience
  • disadvantage of SB method is that the IBNR by yr is dependent upon rate-level adjusted prem
• Method 4: Simple Credibility IBNR estimate
• Method 5: Other Credibility procedures
• Method 6: Alternative estimation methodologies

Question 16

Stanard Buhlmann Method

Answer 16

• SBELR = SB estimate of ELR
• SBIBNR (k) = SB IBNR estimate, year K
• RRL (k) = reported reinsurance loss, year k
• ARPP (k) = adjusted risk pure premium, year k
• Rlag(k) = aggregate claim dollar report lag, year k
• SBELR = ΣRRL(k)/Σ[ARPP(k)*Rlag(k)]
• SBIBNR(k) = SBELR * ARPP(k)*(1-Rlag(k))
• ARPP(k) * Rlag(k) is used up premium

Question 17

Simple Credibility IBNR Estimate (Method 4)

Answer 17

• When we don’t have complete confidence in rate-level prem adjustment, we can weight CL and SB
• Gives more weight to SB for immature years
• GIves more weight to CL for older years
• CredIBNR(k) = credibility IBNR for year k
• CLIBNR(k) = CL IBNR for year k
• CF = credibility factor (between 0 and 1)
• Z(k) = CF*Rlag(k)
• CredIBNR(k) = Z(k) * CLIBNR(k) + (1-Z(k)) * SBIBNR (k)

Question 18

Other credibility procedures (Method 5)

Answer 18

• Weight together IBNR estimates based on reproted and paid claims
  
  • Rptd claims include case reserves that vary over time depending on the claims adjuster
  • Pd claims tend to be more stable
  • Weights could be based on relative claim report and payment lags for each year
• Use ELR inherent in underlying pricing of the exposure in lieu of or in conjunction with the SB ELR
  
  • We call these a priori ELR estimates and can use them as our BF ELR estimates. These can then be used to calculate BF IBNR
  • Weight this a priori IBNR against the CL IBNR

Question 19

Alternative estimation methodologies (Method 6)

Answer 19

• Stochastic Reserving Models
  
  • Gives us more info and provide insight not available with traditional methods
  • They tend to be complicated and black boxish
• Claim Count/Claim Severity Model
  
  • An advantage is that we can build models for various lag distributions and then connect them

Question 20

Monitoring and Testing Predictions

Answer 20

• Monitoring and testing quarterly run off against predictions provides early warning of problems
• For short and medium tailed lines, past AY run-off can be compared with previous year-end reported open reserves and IBNR reserves
• More sophistication for long tailed lines
• If more claims than expected:
  
  • Is it purely random?
  • Was beginning IBNR too small?
  • Were lags too short?
• Continue to monitor and see if it persists