Actuarial Notes

Exam 7

Advanced Estimation of Claims Liabilities (Exam 7) is a 4-hour computer-based exam (4.5-hour Pearson VUE appointment, with a 15-minute scheduled break) covering unpaid claim point estimates, unpaid claim distributions and their diagnostics, and reserving for reinsurance.

Learning Objectives

A. Estimation of Claims Liabilities (100%) Candidates are expected to apply basic Principles and Standards of Practice for unpaid claim estimation, including evaluating liabilities arising in complex risk transfer agreements common in excess insurance and reinsurance contracts.

Data Preparation, Organization, & Analysis

  1. Perform data diagnostic analyses and adjust for data issues.

Unpaid Claim Point Estimates

  1. Calculate unpaid claims estimates.
  2. Test unpaid claim estimates for reasonableness.
  3. Estimate unpaid claims for various layers of coverage.
  4. Forecast premium reserves (e.g., reserves for retrospective premiums).

Unpaid Claim Stochastic Distributions

  1. Estimate parameters of unpaid claims distributions.
  2. Calculate the moments and percentiles of unpaid claim distributions.
  3. Simulate parameter percentiles and unpaid claims percentiles.
  4. Calculate the mean and prediction error of a reserve.
  5. Derive predictive distributions using stochastic methods.

Unpaid Claim Output & Diagnostic Analysis

  1. Test output of unpaid claim distributions for reasonableness.
  2. Test assumptions underlying reserving models.
  3. Develop a range of indications.
  4. Calculate risk margins.

Reinsurance

  1. Adjust primary methods and data to be used for reinsurance reserving.
  2. Calculate ceded loss reserves.
  3. Describe the function and types of reinsurance.

Readings: Brosius · Clark · Friedland · Hurlimann · Mack – Chain Ladder · Mack – Benktander · Marshall et al. · Meyers · Sahasrabuddhe · Shapland · Siewert · Taylor · Teng and Perkins · Venter Factors · Verrall

Source Material

Source Material

  • Loss Development Using Credibility (Brosius - 1993)
    • A1-A3, A6, A11 — CAS Study Note, March 1993
  • LDF Curve-Fitting and Stochastic Reserving (Clark - 2003)
    • A2-A3, A6-A8, A11 — Casualty Actuarial Society Forum, Fall 2003
  • Reserving for Reinsurance (Friedland - 2022)
    • A15-A17 — CAS Study Note, 2022
  • Credible Loss Ratio Claims Reserves (Hurlimann - 2009)
    • A1-A3, A6, A11 — ASTIN Bulletin 39(1), 2009, pp. 81-99, including errata; candidates are not responsible for mathematical proofs
  • Measuring the Variability of Chain Ladder Reserve Estimates (Mack - 1994)
    • A2, A6-A8 — Casualty Actuarial Society Forum, Spring 1994
  • Credible Claims Reserves: The Benktander Method (Mack - 2000)
    • A1-A3, A9, A11-A12 — ASTIN Bulletin, 2000, pp. 333-347
  • A Framework for Assessing Risk Margins (Marshall et al. - 2008)
    • A14 — Institute of Actuaries of Australia 16th General Insurance Seminar, November 2008
  • Stochastic Loss Reserving Using Bayesian MCMC Models (Meyers - 2019)
    • A9-A11, A14 — CAS Monograph #8, 2nd edition, including errata
  • Claims Development by Layer (Sahasrabuddhe - 2010)
    • A4 — Casualty Actuarial Society E-Forum, Fall 2010, Volume 1 (revised January 2, 2013), including errata
  • Using the ODP Bootstrap Model (Shapland - 2016)
    • A1, A9-A11, A13 — CAS Monograph #4, including errata; supplementary modeling files linked on pages 61-62 will aid in understanding of the method's application
  • A Model for Reserving Workers Compensation High Deductibles (Siewert - 1996)
    • A4 — Casualty Actuarial Society Forum, Summer 1996, pp. 217-244
  • Stochastic Loss Reserving Using Generalized Linear Models (Taylor and McGuire - 2016)
    • A9-A12 — CAS Monograph #3, Chapters 1-6, including errata
  • Estimating the Premium Asset on Retrospectively Rated Policies (Teng and Perkins - 1996)
    • A5 — PCAS LXXXIII, 1996, pp. 611-647, excluding Section 5, including the discussion by Feldblum (PCAS LXXXV, 1998, pp. 274-315), Sections 1 and 2 only; candidates will not be held responsible for specific Annual Statement notation but will be responsible for concepts presented
  • Testing the Assumptions of Age-to-Age Factors (Venter - 1998)
    • A2, A6, A12 — PCAS LXXXV, 1998, pp. 807-847, including errata and updated errata
  • Obtaining Predictive Distributions for Reserves Which Incorporate Expert Opinion (Verrall - 2007)
    • A9, A13 — Variance, Vol. 1, Issue 1, 2007, including errata