Meyers Flashcards
Reasons models may not accurately predict distributions of data (3)
- insurance process is too dynamic to be captured by a single model
- other models could better fit data
- data used to calibrate model was missing crucial information (ex: changes in claims handling, underlying business changes, etc.)
Tests for uniformity and descriptions (2)
- histogram - bars of equal height
- p-p plot and Kolmogorov-Smirnov (K-S) test - plots predicted percentiles against expected percentiles and looks for a diagonal line along y=x
K-S test
compare expected vs. model predicted percentiles and set D = max ( abs. value ( difference ) )
reject the null hypothesis of uniformity if D > critical value
Possible test outcomes and interpretations of the histogram and p-p plots (4)
- uniform - relatively flat histogram and p-p plot tightly distributed around diagonal line
- light tailed - histogram is higher at endpoints and p-p plot has an “S shape”
- heavy-tailed - histogram is highest in the center and p-p plot has a “sideways S shape”
- biased high - histogram has the highest frequency at the lowest percentiles, and decreases as expected loss increases; and p-p plot is the curved below the diagonal (right side of a U)
Mack model results on cumulative incurred data
symmetric with light tails
Significance of light tails on model results
understates the variability of the predictive distribution
Bootstrap ODP model results on incremental paid data
non-symmetric and biased high
Significance of being biased high on model results
expected losses will be overstated (b/c actual < expected the majority of the time)
Potential explanations for why neither the Mack incurred or bootstrap paid ODP model validated (2)
- changes in the insurance environment which are not yet observable
- other models exist which can validate
Methods to increase the variability of the predictive distribution (2)
- treat the level of the AY as random
- allow for correlation between AYs (vs. independence)
Mean of the leveled CL model (LCL) - aka mu(w,d)
level of each AY = mu(w,d) = a_w + b_d
a_w = level of log losses for an AY
exp(b_d) = % of losses paid to date
Mean of the correlated CL model (CCL) - aka mu(w,d)
a_w + b_d + p*[ln(C_w-1,d) - mu(w-1,d)]
a_w = log losses in each AY
exp(b_d) = % losses reported
p = correlation coefficient
parenthesis: previous AY cumulative claims - previous AY mean
Description of the leveled CL (LCL) and correlated CL (CCL) methods
LCL: includes a parameter for the level of each AY
CCL: LCL + parameter for correlation between AYs
Relationship between sigma and development age (d) for cumulative vs. incremental losses along with rationale for each
cumulative: as d increases sigma decreases - fewer open claims in later development periods that are subject to random fluctuations
incremental: as d increases sigma increases - smaller, less volatile claims will be settled first
Leveled CL results on cumulative incurred data
improvement over Mack model but still produces light tails
Correlated CL results on cumulative incurred data
model validates despite thin tails
Mack, ODP bootstrap, and CCL method results on incremental paid losses
all biased high
Consequences of using a CY trend (2)
Trend applies to incremental losses so:
- data tends to be right skewed
- occasionally has negative values
Description of correlated incremental trend (CIT) and leveled incremental trend (LIT) methods
CIT - allows correlation between AYs and includes a CY trend parameter (tau)
LIT - CIT without correlation of AYs
Description of the changing settlement rate (CSR) method and loss data used
includes a claim settlement rate parameter
uses cumulative loss data
Mean of the CIT model - aka mu(w,d)
level of AY = mu(w,d) = alpha(w) + beta(d) + tau * (w + d - 1)
correlation is applied by using a mixed lognormal-normal distribution
Mean of the CSR method - aka mu(w,d)
level of AY = mu(w,d) = a_w + b_d * (1 - gamma) ^ (w-1)
CIT and LIT model results
still biased high, no noticeable improvement over Mack or ODP bootstrap methods
CSR model results and explanation
model validates and corrects bias in other models
> > recognizes speedup in claim settlement over time because claims are reported and settled faster due to advancements in technology
