Fisher Retro1 Flashcards

1
Q

aggregate loss distribution:

area under curve, area above max ratable loss, area below min ratable loss

A
  • 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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

table M charge & table M savings

A

expected % of loss in excess of max ratio

expected % of loss short fall min ratio

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

entry ratio curve - Table M with min and max

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

entry ratio curve - Table M

A

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)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

in practice, separate tableM will be built for different risk size groups since

A

variance of aggregate loss distribution will vary by risk size

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

with tables specified in terms of entry ratios and charges, tables are less vulnerable to

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Table M Charges and Risk Size

A
  • 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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

to summarize about errors in insurance charges

A
  1. % error in insurance charges is greatest for large policies with high entry ratios
  2. $ error in insurance charge is greatest for large policies with low entry ratios
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

asymptote approached by very large risks for table M charge and savings

A

φ(r) = max(1-r,0)

ψ(r) = max(r-1,0)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

as risk size goes to 0 for table M charge and savings

A

φ(r) -> 1

ψ(r) ->0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q
  • some policies of even same size are riskier than other policies and should account for this
  • to do this,
A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

basic premium formula derived contains net insurance charge I

when max and min premiums are explicitly selected, net insurance charge depends on

A

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
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

If the minimum premium is increased but the maximum premium and the loss conversion factor remain the same, then the basic premium

A

will decrease because the insurance savings will increase (which is
subtracted as part of the net insurance charge).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

If the maximum premium is decreased but the minimum premium is increased by an equal amount, then the basic premium will

A

the impacts depend on the shape of the aggregate distribution underlying the Table M.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

If the basic premium and loss conversion factor remain the same but the minimum premium increases, then the maximum premium will

A

decrease -> this has to be true for the basic premium to remain constant.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

the difference between the guaranteed cost premium and the retro premium will be driven by

A

the net insurance charge I, which will depend on the selected maximum and
minimum premium.

R-GCP = cIT

If the max and min are selected to result in a zero net charge, then the retro premium will equal the guaranteed cost premium. If the max and min are selected such that there is a positive net charge, the retro premium will be higher than the guaranteed cost premium.

17
Q

why an iterative procedure is used for retro prem

A

The iterative procedure is needed because the insured selects H (minimum premium) and G (maximum premium), instead of rG and rH. Since H and G depend on B, which in turn, depends on H and G, an iterative procedure is needed.

18
Q

Advantages of using vertical slices/disadvantages of horizonal slices

A
  • More natural since it corresponds to the way the data is presented.
  • Easier to understand.
  • Quicker if just need φ(r) for 1 entry ratio.
19
Q

Advantages of using horizontal slices/disadvantages of vertical slices:

A
  • More efficient when calculating φ(r) for multiple values of r.
  • Less time consuming when there are many risks, since vertical slices require dealing with each risk individually.
20
Q

aggregate deductible relationship with table M charge

A

The higher the aggregate deductible, the higher the entry ratio. The higher the aggregate deductible, the lower the probability of losses exceeding that aggregate deductible, which means a lower Table M charge.

21
Q

how the impact of the estimation error on aggregate excess loss adequacy varies between smaller and larger sized risks.

A

The percentage error and dollar error will be greater for the large policies.

For large risks, the curves are flatter, so a change in entry ratio will cause the percentage error in charges to be larger compared to small risks with steeper curves.