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On the Practical Multiline Excess of Loss Pricing Jean-François Walhin Secura Belgian Re

On the Practical Multiline Excess of Loss Pricing Jean-François Walhin Secura Belgian Re Université Catholique de Louvain. Agenda. Motivation Numerical example Mathematical model Conclusion. Umbrella Cover.

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On the Practical Multiline Excess of Loss Pricing Jean-François Walhin Secura Belgian Re

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  1. On the Practical Multiline Excess of Loss Pricing Jean-François Walhin Secura Belgian Re Université Catholique de Louvain

  2. Agenda • Motivation • Numerical example • Mathematical model • Conclusion

  3. Umbrella Cover • Carter (2000, 4th ed) defines : A company will arrange an umbrella cover to protect itself against an accumulation of net retained losses under one or more classes of insurance arising from a single event.

  4. Capital allocation • Two lines of business : Fire and MTPL • Capital allocation for Fire : 500 • Capital allocation for MTPL : 1000 • Global capital allocation : 1200 < 1500 • Benefit of diversification between books of business • Why not using it for XL reinsurance ?

  5. Diversification at insurance level • Reduces allocated capital. • Reduces need of reinsurance. • Corollary : reduces reinsurance costs. • Insurance companies ask for these global protections.

  6. Traditional Fire Cover • Layer 1 : 2000 xs 1000 with 3 reinstatements @ 100% • Layer 2 : 3000 xs 3000 with 2 reinstatements @ 100% • Layer 3 : 4000 xs 6000 with 1 reinstatement @ 100%

  7. Traditional MTPL Cover • Layer 1 : 3000 xs 2000 with unlimited free reinstatements • Layer 2 : 5000 xs 5000 with unlimited free reinstatements • Layer 3 : Unlimited xs 10000 with unlimited free reinstatements

  8. Alternative solution • Layer 1 Fire : 2500 xs 500 with unlimited free reinstatements • Layer 1 MTPL : 4000 xs 1000 with unlimited free reinstatements • Global annual aggregate deductible : 1000 • Not for Fire, not for MTPL, but Global.

  9. Mathematical model

  10. Severity distribution

  11. Frequency distribution

  12. Time of fitting • Distributions have been fitted without any future inflation. • Distributions have been fitted at time of quotation.

  13. Original loss amounts ...

  14. … become indexed loss amount

  15. Indexed loss amount (new)

  16. Discretization

  17. Payment pattern

  18. Incremental Insurer’s payments

  19. Cumulative Insurer’s payments

  20. Cumulative Reinsurer’s payments

  21. Perfect reserves

  22. Overstatement

  23. Insurer’s Incurred Losses

  24. Reinsurer’s Incurred Losses

  25. Stability clause

  26. Stability clause

  27. Interests sharing clause (or ALAE)

  28. Rearithmatization

  29. Panjer’s algorithm

  30. Distribution of aggregate Fire claims

  31. Distribution of aggregate MTPL claims

  32. Distribution of aggregate claims for both lines

  33. Multiline annual aggregate deductible

  34. Expected payments and reserves

  35. Cash flow model

  36. Cash Flows • Paid losses • Variation of loss reserves • Investment income on loss reserves • Commercial premium • Brokerage • Retrocession costs • Administration costs • Variation of allocated capital • Investment income on allocated capital • Tax

  37. Technico-financial rate

  38. Commercial rate

  39. Commercial rate Summary :

  40. Sensitivity analysis

  41. Sliding scale

  42. Conclusion • Interest of ceding companies. • Pricing which takes account of all economic and contractual elements. • Easy sensitivity analysis.

  43. Acknowledgments • Thanks to the committee for inviting me to present the paper at the CAS Ratemaking Seminar. • Thanks for listening to me.

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