FSAP Actuarial Valuation of General Insurance Claims Provisions

1. FSAP Actuarial Valuation of General Insurance Claims Provisions Instituto de Seguros de Portugal 01/02/2006

2. Claims Provisions Summary • Underlying principles • Information reported by insurance undertakings • Supervisory process 3.1. Ratio Analysis 3.2. Statistical Approaches • Responsible actuaries practice

3. Claims Provisions 1. Underlying principles • Adequate claims provisions are essential for the financial soundness of general insurance companies • Claims provisions should correspond to a reasonably conservative estimate of the amount of future payments arising from claims incurred before the valuation date: • Claims Reported to the insurance company • Claims Incurred but Not Reported (IBNR) • Claims Management Costs • Statistical methods are commonly used for the estimation of claims provisions

4. Claims Provisions 2. Information reported by insurance undertakings • ISP supervisory analysis is based on: • Responsible Actuary’s report • Auditor’s appraisal • Run-off triangles (claims paid, claims provision, number of claims) for main LOB’s: • Motor (also by coverage) • Property claims • Liability claims • Workers’ compensation • Temporary incapacity • Long-term assistance • Health • Individual insurance • Group insurance • Other relevant statistical data (e.g. premiums, number of policies, Claims settlement expenses, etc.) • Data quality is crucial

5. Claims Provisions 3. ISP Supervisory Process • ISP pays particular attention to the responsible actuary’s critical analysis of the claims provision estimates • Several ratios are computed and analysed • ISP runs various statistical methods (deterministic and stochastic) to estimate the expected value and variability of the claims provision • A detailed technical and practical manual is available to ISP supervision staff as a guidance for the analysis of claims provisioning (off-site and on-site analysis)

6. Claims Provisions 3.1. Ratio Analysis • Ratios and indicators considered on ISP analysis of claims provisions: • Growth on Premiums • Average Premium • Loss Ratio • Average Cost of New Claims • Average Claims Provision • Claims Frequency • Development of Claims Payments • “Speed” of Process closure • Re-openings • Claims Expenses • Provisioning, including IBNR • Readjustments • Ratios are calculated individually and compared on a static and evolutionary perspective with peer group and market benchmarks

7. Claims Provisions 3.2. Statistical Approaches • The statistical methods’ objective is to project the expected future claims experience, using assumptions based on past data analysis complemented with expert opinion • The analysis should consist of: • Analysis of results (particularly the estimation error), taking into account the theoretical assumptions underlying each model • Analysis of relevant graphs and hypothesis tests to assess each models’ fitness

8. Claims Provisions 3.2. Statistical Approaches (cont.) • Format of a Run-off triangle representing accident year xdevelopment year • Run-off triangles may refer to: • Number of claims • Claims paid (common approach) • Claims incurred, i.e. Claims paid + Claims provision • Aim is to estimate the lower unknown triangle (shaded):

9. Claims Provisions 3.2. Statistical Approaches(cont.) • Deterministic methods • Projection of past claims experience assuming fixed development factors • Provides point estimates of the expected future claims amounts • Various actuarial techniques are available • Stochastic models • Random nature of variables is considered • Generally speaking, the future claims amounts are assumed to follow a specified probability distribution • Allows for the measurement of the estimates variability, essential for the construction of confidence intervals for the estimates • Various actuarial models are available

10. Claims Provisions 3.2. Statistical Approaches (cont.) Statistical Methods available at ISP • ISP has in-house built programs that allow for the automatic testing of the following statistical methods: • Some of the methods consider: • Possibility for inflation correction • Variant approaches based on different assumptions • Advanced refinements to include reparameterization and expert opinion

11. Claims Provisions 3.2. Statistical Approaches(cont.) Statistical Approaches – Example • Results from running the programs for the previous run-off triangle:

12. Claims Provisions 3.2. Statistical Approaches(cont.) Statistical Approaches – Example (cont.) • Simulated empirical distribution of the total claims provision using Bootstrap ODP stochastic model:

13. Claims Provisions 3.2. Statistical Approaches(cont.) Statistical Approaches – Example (cont.) • Goodness-of-fit tests for the Analytic ODP stochastic model:

14. Claims Provisions 3.2. Statistical Approaches(cont.) Statistical Approaches – Example (cont.)

15. Claims Provisions 4. Responsible actuaries practice • The company’s responsible actuary is expected to perform regular valuations of technical provisions (including claims provisions), using whatever methods he considers to be more reasonable • The analysis performed by responsible actuaries involves, in most cases, the use of deterministic methods and, increasingly, the use of stochastic methods • ISP recommendations: • Enhancement of the quality of the information • Estimation of the provision for management costs • Encouragement for the use of stochastic models • Highlight on the importance of testing the assumptions underlying each particular model – there is not an optimal model adjusted for all situations • Importance of the back-testing exercise

16. Claims Provisions Risk oriented approach The supervisory process of claims provisions analysis provides one important input for the global risk oriented framework