Claims Tracking and Monitoring Process for Life Insurance Companies

1. Developing A Claims Tracking And Monitoring Process Shuang Yin, Ph.D. Student at the Department of Statistics Tongan Liu, Masters Student at the Department of Mathematics 09/15/2017

2. Claims Tracking and Monitoring Process • An innovative management tool for life insurance companies. • The insurer can quickly grasp the notion of which types of policyholders (clusters) have required more (or less) claim payouts than expected from the insurer. Cluster Tracking & Monitoring Insurance company

3. What is a Tracking & Monitoring Process • Main features of our algorithm: Efficient, Dynamic and • Flexible. • Efficient: Balance between efficiency and accuracy compared to the exhaustive method. • Dynamic: Does both the current quarter and the historical trend analysis, so management gets the information about the historical performance of a given cluster of policyholders. • Flexible: Historical trend could be tailored to suit the needs of management: we could trace the data back to 24 quarters, 36 quarters etc. • Potential of the algorithm: • Action Steps: Management could make underwriting, reserving and pricing changes accordingly for a company. • Risk control: The claims tracking tool would help management quickly identify where the risk points are and reduce the volatility of the company (good for rating analysts).

4. The Process of Cluster Tracking & Monitoring Warning sign on current quarter Warning sign on historical performance

5. Cluster Analysis (Defined By Clients) Female & Term Two-level clusters Male & Nonsmoker Male & Nonsmoker & VL Three-level clusters Male & Smoker & UL

6. Terminology What is A/E by amount and by count? • A/E by amount = . • A/E by count = .

7. Terminology Historical Performance • What is “significance”? • Statisticallysignificant is the likelihood that a relationship between two or more variables is caused by something other than random chance.  • Current Quarter Slope significantly > 0 and historical average A/E significantly > 1 Significantly good Slope significantly < 0 and historical average A/E significantly > 1 Historical trend line T-test Slope significantly > 0 and historical average A/E significantly < 1 Significantly bad Clusters Z-test Slope significantly < 0 and historical average A/E significantly < 1 Not significant Not significant

8. Example: Data Management Report

9. Example: Management Report—Part 1 (Overall) Overall A/E is tested to be not significant. The mortality expected values were calculated based on 2014 VBT

10. Example: Management Report—Part 1 (Overall)

11. Example: Management Report—Part 2 (Analysis of Significant Clusters)

12. Example: Management Report—Part 3 (Historical Trend Line For Significant Main Cluster B5 For Short Term and Long Term Trend)

13. Example: Management Report—Part 3 (Historical Trend Line For Significant Two-level Cluster A1 & E1 For Short Term and Long Term Trend)

14. What Is A Benchmarking Report • Asisshowninpreviouspages,weareabletocreate amanagementreport,forcurrentquarterA/E andhistoricaltrendlines. • Inthefuture,our purpose is to build individual reportsformultiplecompaniesand rank a company’s A/E relative to its peers. • An individual claims tracking report together with a benchmarking report will help a company understand its own claim experience as well as compare it relative to its peers.

15. Overall A/E In Our Database

16. Individual And Benchmarking Report ForCompanyA

17. Overall A/E Trend In Our Database

18. Term A/E Trend In Our Database

19. Rank Trend ReportForCompanyA

20. Rank Trend ReportForCompanyA

21. ConcludingComments And Next Steps • Individual company claims tracking and monitoring report could use a company’s own expected mortality for A/E analysis. • Benchmarking report should use the same expected mortality for all companies in order to be comparable. • Goldenson Center plans to partner with a third party in order to develop an industry-wide quarterly claims tracking, monitoring and benchmarking system. • Use of a third party ensures company privacy and data confidentiality. • Valuable experiential education for Goldenson Center students. • Valuable information for participating companies. • Could be extended to other actuarial risks like long term care, disability income, variable annuity partial withdrawals, etc.

22. Appendix

23. Cluster Z-test Cluster Z-test (by amount) • : Expected payout of policies. • : Actual payout of policies, • Cluster = , • Test statistics: Z-score = ~ N(0,1) • Hypothesis: E(Cluser) = 1 vs E(Cluster) ≠ 1 • Decision criteria: reject Expected( Cluster )= 1 if p-value = Probability (z > |Z-score|) < 0.05. • Standard Deviation formula: • : Face amount value of policy number k • : Mortality rate of the policyholder, aged x, also notated as • SD(Cluster) = • Variance(Cluster) = =

24. Slope T-test T-test for Trend Line Slope • Construct a simple linear model: • y is the estimate value of A/E, and x is the number of quarters from the starting point. • Hypothesis: = 0 vs ≠ 0 • Test statistic: T-score = ~ t-distribution • Decision criteria: reject = 0 if p-value = Probability (t > |T-score|) < 0.05. T-test for Historical Average A/E • Hypothesis: = 1 vs ≠ 1 • Test statistic: T-score = ~ t-distribution • Decision criteria: reject = 1 if p-value = Probability (t > |T-score|) < 0.05.

25. Second-to-Die Policy Mortality Rate Formula • Second-to-Die mortality rate = Probability{2nd death occurs in the coming year given that at least one life is alive at the beginning of the year} =