Ventor Factors

Question 1

Notations: c(w,d), c(w, inf), q(w,d)

Answer 1

• 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

Question 2

Notations: f(d), F(d)

Answer 2

• 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)

Question 3

What’s the result if the Mack assumptions hold?

Answer 3

Under the Mack assumptions, the Chain Ladder method gives the
minimum variance unbiased linear estimator of future claims emergence.

Question 4

Testable Implications of the Mack Assumptions

Answer 4

Question 5

Alternative emergence patterns

Answer 5

Question 6

Goodness of fit:
Adjusted SSE, AIC, BIC formulas

Answer 6

Question 7

Alternative Emergence Patterns:
Linear with Constant

Answer 7

Question 8

Alternative Emergence Pattern:
Cape Cod

Answer 8

Question 9

Some possible ways to reduce the
number of parameters in a parameterized BF model

Answer 9

• 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

Question 10

Testing Implication 1:
Significance of Factor

Answer 10

Question 11

h(w) and f(d) formulas
with constant variance

Answer 11

Question 12

h(w) and f(d) formulas
with variance ∝ f (d )h(w)

Answer 12

Question 13

Calculating the h factor for the Cape Cod method

Answer 13

Question 14

Ways to improve the Cape Cod fit

Answer 14

• Use a loss ratio triangle
• Adjust loss ratios for trend and rate level

Question 15

What are the assumptions of future loss emergence
for the chain ladder and BF methods?

Answer 15

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.

Question 16

What is the assumption of the Cape Cod and
additive chain ladder methods?

Answer 16

Years with low (or high) losses to-date will have the same expected future
dollar development as other accident years.

Question 17

Testing Implication 3:
Test of Linearity

Answer 17

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

Question 18

Testing Implication 4:
Test of Stability → Residuals over Time

Answer 18

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.

Question 19

Testing Implication 5:
Correlation of Development Factors

Answer 19