Actuarial Notes

Case Study for Individual Risk Rating Study Note

By Ginda Kaplan Fisher et al. · Casualty Actuarial Society · 2019

Study guide: Exam 8

An Excel workbook that accompanies the CAS Individual Risk Rating Study Note. It applies the study note's methods to a single set of fictional claims data, in ten steps: fitting a severity distribution, calculating increased limits factors and excess ratios, and pricing one account under an experience modification, a large deductible plan and a retrospective rating plan, with a limited Table M built along the way.

On the syllabus

  • Exam 8 — objectives B1–B6; Excel file.

Introduction

  • The case study accompanies the study note for the Part 8 exam, and each step has a matching answer sheet.

Step 1

  • Fit a lognormal probability distribution to the claims data, which is equivalent to a maximum likelihood estimator, and compare the fitted mean and standard deviation to the empirical ones.

Step 2

Step 3

Step 4

  • Calculate the premium under a large deductible plan with no aggregate deductible limit, given the expense, premium tax, commission and underwriting profit assumptions.

Step 5

  • Calculate the parameters of a retrospective rating plan with no maximum or minimum, and the retrospective rated premium when actual limited losses equal expected, half expected and twice expected.

Step 6

  • Use the vertical slicing method to calculate the insurance charge for an entry ratio of 2.0 and a deductible or loss limit of $100k, from the annual loss results of 500 risks of the same size.

Step 7

  • Use the horizontal slicing method to calculate a full table of insurance charges, in increments of 0.1 from 0 to 4, and compare the charge at an entry ratio of 2.0 to the Step 6 answer.

Step 8

  • Calculate the insurance charge dollars for Maya Incorporated under a large deductible plan with an aggregate deductible limit and under a retrospective rating plan with a maximum and a minimum ratable loss.

Step 9

  • Recalculate the large deductible premium from Step 4 to incorporate the aggregate deductible limit from Step 8.

Step 10

  • Recalculate the retrospective rating parameters from Step 5 incorporating the maximum and minimum ratable losses from Step 8, and compare the three actual-loss scenarios to the Step 5 answers.

Related readings

  • Individual Risk Rating Study Note (Fisher et al. - 2019) — the study note this case study accompanies

Sources