Fisher Retro1 Flashcards
aggregate loss distribution:
area under curve, area above max ratable loss, area below min ratable loss
- total area under curve is equal to expected losses per policy
- area above max ratable limit asymptote represents expected aggregate losses in excess of max ratable limit
- area below min ratable limit asymptote represents expected shortfall of aggregate losses below min ratable limit
table M charge & table M savings
expected % of loss in excess of max ratio
expected % of loss short fall min ratio
entry ratio curve - Table M with min and max
charge @ rG = D
charge @ rH = C+D
expected retro prem = A+B+C
in balanced plan, E[R]=GCP=(e+E[A])T
minimum prem = A+B
entry ratio curve - Table M
y=A/E[A]
the area under the unlimited loss curve must equal 1
φ (r) = area between horizontal line r and unlimited loss
φ (0) = 1, φ (inf) = 0
ψ (r) = area between unlimited loss and horizontal line r
ψ (0) = 0, ψ (inf) = inf
area from (0,0) to (1,r) = r
r=ψ(r) + 1 - φ(r)
in practice, separate tableM will be built for different risk size groups since
variance of aggregate loss distribution will vary by risk size
with tables specified in terms of entry ratios and charges, tables are less vulnerable to
inflation
-as risk increases in size due to inflation, it can simply be mapped to different existing table M charge column this is more appropriate for its new risk size
Table M Charges and Risk Size
- for smaller risk sizes, majority or risks have no claims at all but small number or risks can have 1 or 2 large claims
- for very large risks, all risks will have claims and experience across all risks becomes more similar as there is less variance in loss experience between risks
- as risk size goes to infinity, variance in entry ratios goes to 0 and curve will flatten to look like all risks have exact same amount of losses
to summarize about errors in insurance charges
- % error in insurance charges is greatest for large policies with high entry ratios
- $ error in insurance charge is greatest for large policies with low entry ratios
asymptote approached by very large risks for table M charge and savings
φ(r) = max(1-r,0)
ψ(r) = max(r-1,0)
as risk size goes to 0 for table M charge and savings
φ(r) -> 1
ψ(r) ->0
- some policies of even same size are riskier than other policies and should account for this
- to do this,
adjust expected losses for risk to match those of a risk with different size but similar variance in aggregate loss distribution
example of this, historically NCCI has adjusted for riskiness differences between states and hazard groups
basic premium formula derived contains net insurance charge I
when max and min premiums are explicitly selected, net insurance charge depends on
max and min premium selected
- max and min premiums also depend on basic premium
- so trial and error procedure called table M search is needed to determine correct Table M rows for rating a policy
If the minimum premium is increased but the maximum premium and the loss conversion factor remain the same, then the basic premium
will decrease because the insurance savings will increase (which is
subtracted as part of the net insurance charge).
If the maximum premium is decreased but the minimum premium is increased by an equal amount, then the basic premium will
the impacts depend on the shape of the aggregate distribution underlying the Table M.
If the basic premium and loss conversion factor remain the same but the minimum premium increases, then the maximum premium will
decrease -> this has to be true for the basic premium to remain constant.