Understanding PEBELS in Liberty Mutual Group Insurance

PEBELS, an innovative approach in Liberty Mutual Group insurance, focuses on Property Large Loss Exposure Segmentation to address challenges like strong regional focus, state/program variations, and high heterogeneity. It involves defining and deriving methodologies for handling various insurance segments with practical considerations. The goal is to develop new applications for effective risk management.

• Liberty Mutual
• Insurance
• PEBELS
• Property Exposure
• Risk Management

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1. Liberty Mutual Group PEBELS: Policy Exposure Based Excess Loss Smoothing Marquis J. Moehring

2. Outline 1. Background 2. Goal 3. PEBELS Defined 4. PEBELS Derived (PPR Generalized) 5. Applications 6. Summary Liberty Mutual Insurance

3. My Challenge Strong Regional Focus State/Program Large Loss Provisions Low Credibility High Heterogeneity Liberty Mutual Insurance

4. This Should be Easier No applicable method in literature ILFs for Liability ELFs for Workers Compensation Nothing for Commercial Property or Homewners! Liberty Mutual Insurance

5. Goal of PEBELS PEBELS = Property Large Loss Exposure Segmentation Meet my challenge New applications! Deceptively difficult 1) No clear limit 2) Multiple non-linearities 3) Additional nuances 4) Practical considerations Liberty Mutual Insurance

6. PEBELS Defined Defined as ??????= ?? ???? ??? ?? ????= ?(??) = ????? ???????? ???? ???= ?(??)-? ?? = ?????????? ???(??)?? ????? Liberty Mutual Insurance

7. Exposure Curve 100% 90% G(Loss / Insured Values) 80% 70% 60% 50% c = 5.0 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Loss / Insured Value Liberty Mutual Insurance

8. PEBELS Derived PEBELS Derived = PPR Generalized Classic Reinsurance Per Risk Exposure Rating Generalized to contemplate, 1) Policy level heterogeneity 2) Expected loss heterogeneity via ???? 3) Loss process heterogeneity via ??? 4) Historical vs. prospective exposure profiles 5) Credibility Liberty Mutual Insurance

9. PEBELS Derived PEBELS Derived = PPR Generalized Classic Reinsurance Per Risk Exposure Rating Generalized to contemplate, 1) Policy level heterogeneity 2) Expected loss heterogeneity via ???? 3) Loss process heterogeneity via ??? 4) Historical vs. prospective exposure profiles 5) Credibility Liberty Mutual Insurance

10. Reinsurance Per Risk Exposure Rating Retention as a % of Insured value Retention + Limit as a % of Insured value Insured Value Range ($000s) Expected Primary Losses Expected Reinsurer Losses Midpoint ($000s) Exposure Factor Subject Premium Expected Loss Ratio 60 167% 833% 0% 682,000 65% 443,300 0 20-100 175 57% 286% 26% 161,000 65% 104,650 27,209 100-250 625 16% 80% 41% 285,000 65% 185,250 75,953 250-1,000 1,500 7% 33% 33% 1,156,000 65% 751,400 247,962 1,000-2,000 2,284,000 65% 1,484,600 351,124 Grand Total Liberty Mutual Insurance

11. PEBELS Derived PEBELS Derived = PPR Generalized Classic Reinsurance Per Risk Exposure Rating Generalized to contemplate, 1) Policy level heterogeneity 2) Expected loss heterogeneity via ???? 3) Loss process heterogeneity via ??? 4) Historical vs. prospective exposure profiles 5) Credibility Liberty Mutual Insurance

12. Per Policy Generalization Insured Value Range ($000s) Retention as a % of Insured value Retention + Limit as a % of Insured value Expected Primary Losses Expected Reinsurer Losses Midpoint ($000s) Exposure Factor Subject Premium Expected Loss Ratio 20-100 60 167% 833% 0% 682,000 65% 443,300 0 100-250 175 57% 286% 26% 161,000 65% 104,650 27,209 250- 1,000 625 16% 80% 41% 285,000 65% 185,250 75,953 1,000- 2,000 1,500 7% 33% 33% 1,156,000 65% 751,400 247,962 2,284,000 65% 1,484,600 351,124 Grand Total Liberty Mutual Insurance

13. PEBELS Derived PEBELS Derived = PPR Generalized Classic Reinsurance Per Risk Exposure Rating Generalized to contemplate, 1) Policy level heterogeneity 2) Expected loss heterogeneity via ???? 3) Loss process heterogeneity via ??? 4) Historical vs. prospective exposure profiles 5) Credibility Liberty Mutual Insurance

14. Heterogeneity Generalization Expected Loss Ratio Retention as a % of Insured value Retention + Limit as a % of Insured value Insured Value Range ($000s) Expected Primary Losses Expected Reinsurer Losses Midpoint ($000s) Exposure Factor Subject Premium 65% 60 167% 833% 0% 682,000 443,300 0 20-100 65% 175 57% 286% 26% 161,000 104,650 27,209 100-250 65% 625 16% 80% 41% 285,000 185,250 75,953 250-1,000 65% 1,500 7% 33% 33% 1,156,000 751,400 247,962 1,000-2,000 2,284,000 65% 1,484,600 351,124 Grand Total Liberty Mutual Insurance

15. Heterogeneity Generalization ??????= ?? ???? ??? Expected catastrophe loss Risk loads Rate adequacy State: House 65.0% X 65.0% Y 40.0% Z Liberty Mutual Insurance

16. PEBELS Derived PEBELS Derived = PPR Generalized Classic Reinsurance Per Risk Exposure Rating Generalized to contemplate, 1) Policy level heterogeneity 2) Expected loss heterogeneity via ???? 3) Loss process heterogeneity via ??? 4) Historical vs. prospective exposure profiles 5) Credibility Liberty Mutual Insurance

17. Heterogeneity Generalization Retention as a % of Insured value Retention + Limit as a % of Insured value Insured Value Range ($000s) Expected Primary Losses Expected Reinsurer Losses Exposure Factor Midpoint ($000s) Subject Premium Expected Loss Ratio 0% 60 167% 833% 682,000 65% 443,300 0 20-100 26% 175 57% 286% 161,000 65% 104,650 27,209 100-250 41% 625 16% 80% 285,000 65% 185,250 75,953 250-1,000 33% 1,500 7% 33% 1,156,000 65% 751,400 247,962 1,000-2,000 2,284,000 65% 1,484,600 351,124 Grand Total Liberty Mutual Insurance

18. Exposure Curve 100% 90% G(Loss / Insured Values) 80% 70% 60% 50% c = 5.0 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Loss / Insured Value Liberty Mutual Insurance

19. Exposure Curve Dispersed: e.g. Estate / University Campus 100% 90% G(Loss / Insured Values) 80% 70% 60% 50% c = 5.0 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Loss / Insured Value Liberty Mutual Insurance

20. Exposure Curve Dispersed: e.g. Estate / University Campus 100% 90% G(Loss / Insured Values) 80% 70% 60% C = 1.5 50% c = 2.0 c = 3.0 40% c = 4.0 c = 5.0 30% 20% Concentrated: e.g. Barn / Minimart 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Loss / Insured Value Liberty Mutual Insurance

21. PEBELS Derived PEBELS Derived = PPR Generalized Classic Reinsurance Per Risk Exposure Rating Generalized to contemplate, 1) Policy level heterogeneity 2) Expected loss heterogeneity via ???? 3) Loss process heterogeneity via ??? 4) Historical vs. prospective exposure profiles 5) Credibility Liberty Mutual Insurance

22. PEBELS Derived PEBELS Derived = PPR Generalized Classic Reinsurance Per Risk Exposure Rating Generalized to contemplate, 1) Policy level heterogeneity 2) Expected loss heterogeneity via ???? 3) Loss process heterogeneity via ??? 4) Historical vs. prospective exposure profiles 5) Credibility Liberty Mutual Insurance

23. Applications Indications Motivated PEBELS Allocate large losses to state and program Low credibility High heterogeneity in underlying exposures Liberty Mutual Insurance

24. Applications Adjusted Modeled Catastrophe AALs Traditionally assume AAL linear with IV This contradicts Theory presented Ludwig s study of Hurricane Hugo Implies bias between Personal & Commercial Can adjust AALs with PEBELS Liberty Mutual Insurance

25. Applications Predictive Models Hypothesize that PEBELS More predictive of large loss than IV Most predictive for highly skewed perils Most predictive in severity/excess models Liberty Mutual Insurance

26. Applications Revised Property Per Risk Reinsurance Exposure Rating Current formulation: ???????? ??????????? ?????????? ??????? ???????? ??? ?? ????? = ???????????? ????? ????? ??????????? ???????? ???????? ??? ?? ????? ??????????? ????????????? ????? ????? Liberty Mutual Insurance

27. Applications Revised Property Per Risk Reinsurance Exposure Rating Proposed formulation: ???????? ??????????? ?????????? ) * ??????? ???????? ??? ?? ????? = (???????????? ????? ????? ??????????? ?????????? ???????? ???????? ??? ?? ????? ???????? ???????? ??? ?? ????? (???????? ???????? ??? ?? ????? ????????????? ????? ????? ) ( ) ?????????? ??????????.?????????? Liberty Mutual Insurance

28. Summary PEBELS = Property Large Loss Exposure Segmentation Only game in town Quantifies messy non-linearities Multiple applications Indications Catastrophe Modeling Risk Segmentation Liberty Mutual Insurance

30. Historical vs. Prospective Selecting exposure profile for the application? Prospective (current inforce) Catastrophe modeling Reinsurance quotes Historical ( earned over experience period) Loss ratio ratemaking Revised per risk reinsurance exposure rating Liberty Mutual Insurance

31. Historical vs. Prospective Loss ratio ratemaking examples 1) State in run-off scenario 2) State newly entered scenario Both scenarios lead to skewed state indications Even small shifts will distort indications Liberty Mutual Insurance

32. Credibility Indications example Layer experience to maximize credibility Complements ?????????? ?????$0.5? ?? ???????? ?????$0.1? ?? $0.5? ?????????? 1) ????$0.1? ?? $0.5? ?????????? ?????? ?? ?????.???? (????????? ? ???) 2) Liberty Mutual Insurance

33. Appendix Misc. Topics Exposure curve considerations Data limitations and NLE Methods in common usage Liberty Mutual Insurance