1. March 30, 2016 Christopher M. Holt, ACAS, MAAA Consulting Actuary Introduction to Margins in P/C Reserving

2. 1 Associate of the Casualty Actuarial Society 16 years of industry experience 4 years with Pinnacle About the Presenter

3. 2 ASOP 41 and 43 Development Method Margin Method 1 – Selected Range Margin Method 2 – Varying Development Margin Method 3 – Simulation Margin Method 4 – Mack Method Summary of Methods Graph of First Development Period Margin Method 4 – Mack Method (revisited) Issues References Agenda

4. 3 ASOP 41- Actuarial Communications – In the actuarial report, the actuary should state the actuarial findings, and identify the methods, procedures, assumptions, and data used by the actuary with sufficient clarity that another actuary qualified in the same practice area could make an objective appraisal of the reasonableness of the actuary’s work as presented in the actuarial report. ASOP 43 – Unpaid Claim Estimates – 3.3a - the intended measure of the unpaid claim estimate – 2.1 Actuarial Central Estimate—An estimate that represents an expected value over the range of reasonably possible outcomes. ASOP 41 and 43

5. 4 The distinguishing characteristic of the development method is that ultimate claims for each accident year are produced from recorded values assuming that future claims’ development is similar to prior years’ development. In this method, the actuary uses the development triangles to track the development history of a specific group of claims. The underlying assumption in the development technique is that claims recorded to date will continue to develop in a similar manner in the future – that the past is indicative of the future. Development Method

6. 5 Development Triangle C(i, k) = cumulative losses for accident year I and development period k f(i, k) = Report-to-Report factor for the ith accident year and kth development period f(i, k) = C(i, k+1) / C(i, k) f(2011, 1) = 1.205 [= 16,828 / 13967]

7. 6 Development Triangle – Report-to-Report Factors RTR = Report –to-Report Factors, f(i, k) f(k) = Vol Wgt Ave LDF = loss development factor LDF(j) = product of f(k) for k>=j LDF(9) = 1.057 [= 1.04 x 1.017 x 1.000]

8. 7 Method 1 - Simple Range IBNR = Incurred But Not Reported IBNR (reserves R(i)) = Projected Losses – Incurred Losses

9. 8 Method 2 – RTR Version 2

10. 9 Development Triangle – RTR Version 2

11. 10 Method 3 - Frequency/Severity Model

12. 11 Assumptions – E(C(i+1, k) | C(i, 1), …. C(i, k)) = g(k) x C(i, k) – {C(i, 1), …. C(i,k)} and {C(j, 1), …. C(j, k)} are independent Results – f(k) = sum of C(i, k+1) / sum of C(i, k) is unbiased and uncorrelated – The mean squared error of the Reserve can be estimated by Method 4 – Mack Method

13. 12 Method 4 – Mack Method

14. 13 Method 4 – Mack Method

15. 14 Summary of Methods

16. 15 Graph of Year 2 vs Year 1 Slope = 1.241 R-square = 0.99 Excludes point at 2,098

17. 16 Method 4 – Mack Method (Revisited)

18. 17 Accident year independence Tail factors Variance for tail factors Consistent with standard techniques Multiple methods are used to estimate ultimates Issues

19. 18 Mack Method – Distribution-Free Calculation of the Standard Error of Chain Ladder Reserve Estimates by Thomas Mack, 1993 – Chain Ladder Reserve Risk Estimators by Daniel Murphy, 2007 Development Methods – Estimating Unpaid Claim Using Basic Techniques by Jacqueline Friedland, 2010 References

20. 19 Commitment Beyond Numbers Thank You for Your Attention Christopher M. Holt, ACAS, MAAA Consulting Actuary 678-894-7265 cholt@pinnacleactuaries.com