Describe the steps to complete the Case Development method (Method #1)?

Bedford Estimating Unpaid Claims Using Basic Techniques Seminars Chapter 12 – Case Outstanding Development Technique

Start with the Case Outstanding and Incremental Paid triangles.

  1. Calculate Incremental Paid to Beginning Case ratios—make selections for each age.
  2. Calculate Case to Previous Case ratios—make selections for each age.
  3. Use the selected Case/Previous Case ratios from Step 2 to fill in the bottom half of the Case O/S triangle.
  4. Use the selected Incr. Paid/Begin. Case ratios from Step 1, multiplied by the Case O/S in Step 3 to fill in the bottom half of the Incremental Paid triangle.
  5. Sum up the incremental payments to find the cumulative payments and ultimate claim estimate.

What are the assumptions, appropriate situations to use, advantages, and disadvantages of the Case Development method (Method #1)?

Bedford Seminars

Assumptions: future claims are related consistently to claims already reported.

This method is most stable/appropriate when most claims are reported in the first year, so that it can more accurately measure the incremental paid to prior case ratio. If there are significant new reports in future periods, this ratio will not be as steady due to more moving pieces. This is because future payments include those included in prior case, but also payments on newly reported claims.

Advantages: useful when most claims are reported in the first year, or when evaluating report year triangles.

Disadvantages: most lines of business, on an AY basis, have significant reports after the first year. Additionally, there are no industry benchmarks to compare our selected ratios by age to, and these selections are not necessarily intuitive or something the actuary would have gained knowledge of through general experience. As a result, this method is not commonly used by actuaries.

What are reasonable values, or ranges of values, for the tail factors of each of the two triangles we use in the first Case Development method (Method #1)?

Bedford Seminars

Case to prior case: we select a tail factor of 0.00, implying there are no case reserves after the latest age in the triangle which is the default selection in this method. If we had selected a tail factor greater than 0.00, there would be case reserves in the To Ult column, but that would not lead anywhere since it never becomes the prior case reserves in the next.

Incremental paid to prior case: Our selection represents the percentage of case outstanding at the latest age that is ultimately paid out. As such, it could theoretically be any number>0, but something close to 1.0 is more realistic.

When is the second Case Development method presented in the text useful, and how do you perform it (Method #2)?

Bedford Seminars

Method #2 is useful if the only piece of information we have available is the current case reserves. We could then use industry CDFs and the formula below to develop an unpaid claim estimate. Add reported claims to find the ultimate claim estimate.

Formula:
Reported CDF - 1.00 x Paid CDF Unpaid Claims = Case Reserves + 1 Paid CDF - Reported CDF

What is an alternative formula that can be used to complete the second Case Development method, which is more intuitive (Method #2)?

Bedford Seminars

Though the algebra is not obvious, the above formula is equal to the following formula, which is more commonly used in practice, and accepted by the CAS (see Fall 2016, Q19 Part a, Sample Answer 2):
1 - 1/Paid CDF Unpaid Claims = Case Reserves 1/Rep. CDF - 1/Paid CDF

Which is more intuitive to me since it is equal to:
% Unpaid Unpaid Claims = Case Reserves %Reported - %Paid

Where Case Reserves divided by % Case is an ultimate estimate, which is then multiplied by % Unpaid to estimate Unpaid Claims.

What is the advantage and disadvantages of the second Case Development method (Method #2)?

Bedford Seminars

Advantage: we are able to develop an estimate of unpaid claims when the only piece of information we have is case outstanding (and industry CDFs).

Disadvantages: since this method is used when historical data and company CDFs are not available, we must use industry benchmarks which may prove to be inaccurate for the specific company. It may not be a good estimate for more recent years, if CDFs are highly leveraged. Additionally, any individual large losses contained in the case reserves may distort the projection.