Teng & Perkins Flashcards
Premium asset
premium that insurer expects to collect based on expected ultimate loss experience – prem insurer has already booked = EBNR
*in order to calc, must determine how premiums develop as losses develop -> PDLD ratio
retro reserve
retro reserve = -(prem asset)
once relationship between prem and loss isdetermined, can
be applied to expected future loss development to obtain expected future prem development
premium formula
PDLD1 formula
cumulative loss capping ratio
what are capped losses
-losses that contribute to additional premium (> retro min and < retro max)
-diff between capped and uncapped loss can be viewed as portion of losses outside boundaries of retro min and max
why does loss capping ratio decrease as data becomes more mature
since increasing proportion of loss development occurs outside of limitations
PDLD2: what it refers to and formula
2nd PDLD refers to incremental prem developed between 1st and 2nd retro adj divided by increm loss developed between 1st and 2nd
advantage of using retro formula to estimate PDLDs
-responds to/reflects changes in retro rating parameters that are sold & more stable than those from empirical data
If parameters change significantly over time,
more weight should be given to PDLD ratios derived from formula than hist data
disadvantage to using retro formula and what should you do to test for this
- dis = potential bias exists since formula uses average parameters for LCF, TM, max, min, and per accident limitation
- >Should retrospectively test PDLD ratios against actual emergence to check for bias
empirical approach for PDLD
- need booked premium and reported loss development
- 1st retro prem computation is based on losses development through 18 months and premium booked through 27 months
- premium lag of 9 months is assumed
- subsequent retro adj would occur in annual intervals
why historical PDLD ratios may fluctuate significantly after 1st retro adj
and what should you do?
- prem and loss development on few policies may drive total increm development
- should take average over as many policy periods as possible but pay attention to any trends in PDLD ratios over time
- could also use PDLD ratio calculated from retro formula
upward trend in PDLD
- more liberal retro rating parameters such as higher max, min or per accident limitation
- improvement in loss experience resulting in larger portion of losses being within boundaries of retro max and per acc limitation
Historical and formula PDLD ratios could diverge
- worse or better than expected loss experience may have caused larger portion of loss to be outside or inside boundaries
- average retro parameters may be changing over time
How could you have positive adjustment?
-losses occurring within loss limits
How could you have 0 adj with increm loss?
-all development occurred outside of loss limits
How could you have neg adj with incremental loss?
-losses on claims below loss limits decreased and losses on claims above loss limits increased; if increase in above cap > decrease in losses below cap, then increm prem would drop despite increm loss
cumulative PDLD
- CPDLD ratio is average of PDLDs in all subsequent retro period weighted by percentage of losses to emerge in each period
- CPDLD tells insurer how much prem they can expect to collect for each of dollar of loss that has yet to emerge
what do you need to calc to estimate the premium asset
cumulative PDLD ratios
CDPLD @ 1st adj normally > 1
First retro prem calc includes BP
Only small portion of loss is limited at this point
Application of LCF and TM results in more than $1P per $1L
at subsequent adjs, CPDLD ratio should be less than 1 due to
retro max and per accident limitation
to get future premium
CPDLD * expected future loss emergence
future losses = ult loss – loss reported at prior adj for each PY
CPDLD formulas
premium asset formula
prem asset = expected future prem + prem booked from prior adj – prem booked to date
retro prem composed of 2 parts
- Covers incd loss, LAE, state taxes, and other state assessments = LCF*limited incd loss *TM (LCF mostly covers LAE)
- Covers company expenses, insurance charge, state taxes, and other state assessments = (expense provision + ins charge + excess loss charge)*TM
Combine these to get BP*TM
insurance charge is
difference between expected loss to insurer caused by max retro prem and expected gain caused by min
as BoB matures, prem responsiveness
declines
as time goes by, more losses should be capped by max prem and loss limit
at higher LR, prem responsiveness
declines
Push to settle small claims impact on PDLD
-settling small claims faster will increase both losses and capped losses by same amount -> earlier PDLD ratios will be high because each claim will create add. prem but at later maturities, larger claims will be above cap and will not create add. prem -> PDLD line segment will start steeper but become flatter faster
Why not estimate the accrued retro premium asset using CL on historical triangles of either collected premium or billed premium?
-Due to the lag in processing and recording retro premium adjustments, CL estimate of the premium asset is not available until at least 9M after the policy expiration, and it can be updated only annually thereafter
Using Fitzgibbon’s method or PDLD, an initial estimate of the premium asset can be produced
soon after the policy expires, using the known loss information and the relationships between incurred losses and retro premium
-premium asset estimate can be updated each quarter as new loss data becomes available
reported losses vs retrospective premium graphs: problem with first line segment
*by going through origin, combine basic premium ratio and slope of first line segment
- problem = we cannot tell how much each item contributes to total slope of first line segment and basic premium does not represent emerged losses
- Feldblum says it should be intercept where b=CPDLD1-avg basic prem charge (as ratio to standard loss ratio)
transform cumulative loss capping ratios to incremental loss capping ratios
total retrospective premium asset using enhanced PDLD method as described by Feldblum
*only CPDLD1 changes
*ultimate prem for PY @ 1st retro adj = expected future prem from loss + basic prem portion for 1st Adj
no prem booked at prior adjustment since this is 1st adj
enhanced PDLD changes ultimate prem by taking basic prem portion out of CPDLD1
why does enhanced method produce lower premium asset?
ultimate reported loss is lower than a priori expected ultimate loss calculated with standard premium and ELR
be clear on the exam about loss capping ratios
clearly state if you are using incremental or cumulative loss capping ratios is problem is not explicit
ie say you assume they are giving you incremental info
