Friedland Chapter 15 - DC Insurer monitoring (Exhibit IV)

[EKtheSage]

Summary

• Add docs/friedland/chapter_15_monitoring.ipynb recreating Friedland Exhibit IV Sheets 2-4: selected ultimates at 12/31/2007, then annual and monthly actual-versus-expected reported claims.
• Uses DevelopmentConstant / Chainladder for the Sheet 2 ultimates and the printed reporting-pattern formula for expected emergence. No new sample CSV — Sheet 1's quarterly triangle is not required for the monitoring tests.
• Independent of Friedland Chapter 15 - Evaluation of Techniques (comparison tables) #1220 (comparison tables) and of the Chapter 7-10 JSON estimators.

Related to #588.

Test plan

• pytest --nbmake docs/friedland/chapter_15_monitoring.ipynb
• Confirm AY 2007 ultimate is 2,798 and expected CY 2008 reported is 332
• Confirm AY 2006 expected emergence is 3
• Confirm interpolated Jan/Feb 2008 percent reported for AY 2007 is 91.5% / 95.0%

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[henrydingliu]

• does dc insurer need to be added as a sample dataset?
• calculating expected for the next calendar period is a relatively common task. do you think we need to add it as a property/method of Triangle?

[EKtheSage]

On the two questions:

DC Insurer as a sample dataset. I would not add one in this PR. Sheets 2-4 only use the 12/31/2007 latest diagonal and the selected CDFs. The quarterly triangle in Sheet 1 was not reconstructable from the PDF extract, and the other Friedland samples exist because those chapters reuse the full triangle. Shipping friedland_dc_insurer would be CSV + _manifest.py + load tests + the sample-data table, which is library surface rather than this docs slice. If someone later has a clean Sheet 1 reconstruction, that can be its own sample PR.

Expected emergence as a Triangle property/method. I would not add one here either. Fitted objects already expose the next-period expected:

• full_expectation_ — expected cumulative at each age
• full_triangle_ — actuals plus expected runoff
• model_diagnostics() — Run Off 1/2/3... from full_expectation_

Friedland's formula is the incremental expected from full_expectation_.cum_to_incr() at the next lag. Sheet 4 is the part that is not a general Triangle grain: it interpolates percent-reported between quarterly knots for monthly A/E. That helper stays in the notebook. A dedicated API would be a separate issue with tests and docs, not this notebook.

[henrydingliu]

The quarterly triangle in Sheet 1 was not reconstructable from the PDF extract

this is not true. Based on the selected tail factor, we can safely assume there's no development beyond 36 months

and the other Friedland samples exist because those chapters reuse the full triangle

this is also not true. there are single diagonal datasets from chapter 8 that are loaded as sample data.

Fitted objects already expose the next-period expected:

please use the fitted object in the exhibit. the point is to use chainladder objects to produce matching exhibits, rather than demonstrating pandas manipulation.

[EKtheSage]

Those two claims were wrong. Chapter 8 already ships single-diagonal samples (friedland_auto_bi_insurer), and a 1.000 CDF at 36 months is enough to finish the development pattern.

Pushed a follow-up that:

• adds friedland_dc_insurer with the 12/31/2007 and 12/31/2008 reported diagonals
• takes Sheet 3 expected emergence from the fitted Chainladder model (full_triangle_.dev_to_val() at 2008 minus the 2007 latest_diagonal)

Sheet 4 still interpolates the quarterly percent-reported pattern because the sample is annual grain. No new Triangle method. full_triangle_ already does the next calendar period.

[henrydingliu]

• general
  • weird characters in the headers
• sheet 1
  • can you please add the full triangle to the repo and recreate this exhibit?
• sheet 2
  • please try model_diagnostics to reduce amount of numpy and pandas manipulation
• sheet 4
  • i'm good with this, but will raise a separate issue to add interpolation functionality