Actuarial Notes

Credibility Methods Applied to Life, Health, and Pensions

By David B. Atkinson · Society of Actuaries · 2019

Study guide: Exam ILA-101

A February 2019 Society of Actuaries paper, subtitled Credibility Applications for Life and Health Insurers and Pension Plans. It aims to promote more informed applications of credibility methods for life insurers and pension plans, giving an overview of the most common credibility methods (limited fluctuation and greatest accuracy) and a review of the relevant credibility literature.

On the syllabus

  • Exam ILA-101 — pp. 1-25 only, with the Credibility Methods Companion Excel Files; outcomes 2c.

Preface

  • Purpose
  • Acknowledgements
  • Background and Scope

1 Overview of Credibility

  • 1.1 Credibility Methods
  • 1.2 General Formula for Credibility Methods

2 Limited Fluctuation Method

  • 2.1 Relevance of Prior Rate
  • 2.2 Square Root Formula
    • 2.2.1 Full Credibility
    • 2.2.2 Derivation of the Number 1,082
    • 2.2.3 Counterpart of 1,082 for Mortality and Lapse Risks
  • 2.3 Asymptotic Formula
  • 2.4 Credibility Weights Based on Confidence Intervals
  • 2.5 Mortality Study Example
    • 2.5.1 Mortality Study Data and Results
    • 2.5.2 Determination of Threshold for Full Credibility
    • 2.5.3 Calculation of Credibility-Weighted Rate
  • 2.6 Credibility Applied to Mortality Ratios
  • 2.7 Strengths and Weaknesses

3 Greatest Accuracy Method

  • 3.1 Bayesian Credibility, Stepping Stone to Greatest Accuracy
  • 3.2 Overview of Greatest Accuracy
  • 3.3 Greatest Accuracy Formulas
  • 3.4 Bühlmann-Straub Model
  • 3.5 Estimating the Components of K
  • 3.6 Strengths and Weaknesses

4 Recommended Credibility Readings

  • 4.1 Foundations of Casualty Actuarial Science
  • 4.2 Credibility Practice Note, American Academy of Actuaries, July 2008
  • 4.3 Credibility Theory Practices, SOA Report, December 2009
  • 4.4 Other Recommended Readings for Life, Health, and Pensions
  • 4.5 Other Recommended Readings from Casualty Actuarial Practice

Appendix A Calculation of E[Var[X]] and Var[E[X]]

  • A.1 Weights, Means, and Variance
  • A.2 Portfolio Statistics

Appendix B Minimizing Mean-Squared Error

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