Ventor Factors Flashcards
Notations: c(w,d), c(w, inf), q(w,d)
- c(w, d) = cumulative loss from AY w as of age d
- c(w,inf) = total loss from AY w when end of triangle is reached (no tail factor is included)
- q(w, d) = incremental loss for AY w from d − 1 to d
Notations: f(d), F(d)
- f(d) = factor applied to c(w, d) to estimate q(w, d + 1) (incremental % paid)
- F(d) = factor applied to c(w, d) to estimate c(w,inf) (CDF)
What’s the result if the Mack assumptions hold?
Under the Mack assumptions, the Chain Ladder method gives the
minimum variance unbiased linear estimator of future claims emergence.
Testable Implications of the Mack Assumptions
Alternative emergence patterns
Goodness of fit:
Adjusted SSE, AIC, BIC formulas
Alternative Emergence Patterns:
Linear with Constant
Alternative Emergence Pattern:
Cape Cod
Some possible ways to reduce the
number of parameters in a parameterized BF model
- Use the Cape Cod method
- Use a trend line through the BF ultimate loss parameters to reduce accident year parameters to two instead of one for each year.
- Group years with similar loss levels and fit an h parameter for each group.
→ Can also group f parameters for ages with similar development factors
Testing Implication 1:
Significance of Factor
h(w) and f(d) formulas
with constant variance
h(w) and f(d) formulas
with variance ∝ f (d )h(w)
Calculating the h factor for the Cape Cod method
Ways to improve the Cape Cod fit
- Use a loss ratio triangle
- Adjust loss ratios for trend and rate level
What are the assumptions of future loss emergence
for the chain ladder and BF methods?
Chain Ladder assumption
Assumes future emergence is proportional to losses emerged to-date for a
given accident year.
BF assumption
Assumes expected emergence in each period is a percentage of ultimate loss.
* Regards losses emerged to-date as a random component that doesn’t influence future development.
o If this is the case, using the chain ladder will apply factors to the random component and increase error.
What is the assumption of the Cape Cod and
additive chain ladder methods?
Years with low (or high) losses to-date will have the same expected future
dollar development as other accident years.
Testing Implication 3:
Test of Linearity
Plot the residuals of incremental losses against prior cumulative loss.
If residuals show non-linearity (e.g. positive-negative-positive pattern), the
test fails.
-> If there’s non-linearity, this suggests emergence is a non-linear
function of losses to-date
Testing Implication 4:
Test of Stability → Residuals over Time
Plot the age-to-age factors against time (accident year).
If stable:
All AYs should be used to calculate development factors to reduce the effects of random fluctuations and minimize variance.
If unstable (factors are changing over time):
Use a weighted average of factors with more weight to the recent years.
Testing Implication 5:
Correlation of Development Factors
