Brosius

Question 1

Describe a situation in which it would be appropriate to use the link ratio method, the budgeted loss method and the least square method

Answer 1

1. Link ratio : Use for older accident years where loss development is stable
2. Budgeted loss : Use when fluctuation in loss experience is extreme and/or when past data is not available
3. Least square: Use when random year to year fluctuations in loss experience is significant.

Question 2

What are the special cases of the least square development method

Answer 2

1. Link ratio : a = 0
2. Budgeted loss method when b = 0
3. Bornhuetter-Fergusson method when b = 1

Question 3

Why the flexibility of the least square method gives an important advantage?

Answer 3

Since it gives more or less weight to the observed value of x as appropriate (i.e. credibility weighting)

Question 4

Name 2 issues that can lead to values of a and b that do not reflect reality

Answer 4

1. Significant changes in the nature of the loss experience

2. Sampling error

Question 5

Which method should we use when a < 0 ? b < 0%

Answer 5

1. When a < 0, our estimate of y will be negative for small values of x –> Link ratio
2. When b <0, our estimate of y will decreases as x increases –> Budgeted loss method

Question 6

Name 3 possible solutions for managing the bulk reserves when the reported proportion of expected losses for the current AY period is 8% higher than it should be

Answer 6

1. Reduce the bulk reserve by a corresponding amount (Budgeted)
2. Leave the bulk reserve at the same % level of expected losses (BF)
3. Increase the bulk reserve in proportion of the increase of actual reported over expected reported (link ratio)

Question 7

List the formulas for Q(x) and R(x) for a simple model and Poisson-binomial model. Which method correspond the best to the model?

Answer 7

Simple : Least square

Poisson - Binomial : BF

Question 8

Name the 4 options for link ratios when using the poisson-binomial model

Answer 8

1. Unbiaised estimate
2. Minimize MSE
3. Use E[Y|X]for c
4. Salxmann’s iceberg technique

Question 9

Name formula for Q(X) and R(X) for negative binomial, fixed prior case and fixed reporting case

Question 10

It is difficult to compute a pure bayesian estimate Q since it requires knowledge of the loss and loss reporting processes. We can then use the best linear approximation. What are the 3 advantages?

Answer 10

1. Simpler to compute
2. Easier to understand and explain
3. Less dependent upon the underlying distribution

Question 11

Write the development formula 1. Explain the 3 different scenarios with COV(X,Y) and VAR(X)

Question 12

Write the development formula with empirical data

Question 13

When the least square development is not appropriate? What can we do with systematic distortions?

Answer 13

1. Least square fit does not make sense if year to year changes in loss experience are due largely to systematic shifts or distortions in the book of business
2. May fit if year to year changes are due largely to random chances
3. In the case of systematic distortions, data can be adjusted before applying the least square
   1) Correct for inflation by putting the years on a constant-dollar basis before fitting a line (Incurred losses)
   2) If the business expands, we can divide each year’s losses with exposure to eliminate distortions

Question 14

Write development formula 2 (Credibility weighintg)

Question 15

Write the 3 special cases of the development formula 2

Question 16

Write to formula when we want to estimate VHM and EVPV

Question 17

Write the formula with caseload effect