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INTRODUCTION TO REINSURANCE EXPERIENCE AND EXPOSURE RATING

INTRODUCTION TO REINSURANCE EXPERIENCE AND EXPOSURE RATING. SUMMARY AND RECONCILIATION OF ESTIMATES MICHAEL E. ANGELINA - TOWERS PERRIN CAS RATEMAKING SEMINAR MARCH 11, 2004 PHILADELPHIA, PA. KEY ASSUMPTIONS.

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INTRODUCTION TO REINSURANCE EXPERIENCE AND EXPOSURE RATING

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  1. INTRODUCTION TO REINSURANCEEXPERIENCE AND EXPOSURE RATING SUMMARY AND RECONCILIATION OF ESTIMATES MICHAEL E. ANGELINA - TOWERS PERRIN CAS RATEMAKING SEMINAR MARCH 11, 2004 PHILADELPHIA, PA

  2. KEY ASSUMPTIONS You are the underwriter/actuary of the assumed reinsurance division, what should you be thinking about: • Hazard group selection • Loss ratios • Expense loadings • Claim frequencies • Tail factors • Layer severities • Credibility of experience • Results of u/w audit

  3. Reconciliation of Estimates • Goal - determination of a final estimate Expected Ultimate Excess Recap of results CountsLoss & ALAESeverity • Exposure Estimate 2.3 82.1 28.0 • Classical Burning Cost 1.09 68.4 15.9 • Freq/Severity-Industry 0.85 69.5 12.3 • Experience Estimate 0.96 67.7 14.2 • Wide range of results between experience and exposure • Severity relatively flat • Variation in expected counts/losses

  4. Experience Rating - Frequency Based MethodProjected # of Claims for Rating Year

  5. RECAP OF ESTIMATESUltimate Losses

  6. RECAP OF ESTIMATESExpected Counts > $100k

  7. Reconciliation of Estimates • Which method yields best estimate? • Experience estimates • Test at lower layers • Results for frequency/severity and burning cost should be consistent • Considerations • credibility of data - 40 XS claims? • loss development factors - reflecting claim audit? • load for ALAE (explicit/implicit?) • adjust for claim impact of premium growth - deterioration in U/W? • account for change in policy limits?

  8. Reconciliation of Estimates • Which method yields best estimate (con’t) • Exposure estimates • Allocation of premium consistent with company’s • Historical comparison of XS premium to losses • suggest different loss ratio for layer? • Considerations • appropriateness of size of loss curve • test with claim emergence at different attachment points • calculate implied claim counts to company experience • compare industry curve to company fitted curve • fitting curve is not trivial (development on individual claims) • adequacy of loss ratio • reflect claim audit findings • adjust for implication on growing business • account for differences in excess layer vs. primary layer

  9. Reconciliation of Estimates

  10. Reconciliation of Estimates

  11. Audience Underwriting Recap of Results Ultimate Exp Counts ALAE Implied Loss & ALAE >100kLoadXS L/R Exposure 2.30 28.0 21% 62.1% Burning Cost 1.09 15.9 8.5% 31.8% Frequency/Severity 0.85 12.3 7.5% 24.6% (Industry) Experience 1.00 14.0 8.0% 29.1% * assumes premium allocated to layer is 3,717 (from exposure method)

  12. Reconciliation of Estimates • Goal - Sensitivity test indications • Experience Indications (burning cost) • Selected 1,000 2.5% • Alter Selection 1,200 BF: 2 recent yrs • ALAE Differences 111 18% vs 8% • Revised Selection 1,311 3.3% • Experience Indications (frequency / severity) • Selected 851 2.4% • Alter Selection 1,080 Different weights • ALAE Differences 105 18% vs 7.5% • Revised Selection 1,185 3.0% • Final Selection 1,250 3.1%

  13. Reconciliation of Estimates • Goal - Move expected ultimates to similar base • Exposure Indications • Selected 2,304 5.8% • Alter Selection 1,593 higher % Table 1 • ALAE Differences (40) 18% vs 21% • Revised Selection 1,553 3.9% • Experience Indications (Selected) • Revised Selection 1,250 3.1% • implied loss ratio for layer 34.4% • Final Selection 1,450 3.625% • implied loss ratio for layer 39%

  14. Reconciliation of Estimates Scenario Testing • Move away from point estimate of methods and look at a range of possible outcomes • Exposure • size of loss table/loss ratio • what assumptions would get result to experience rate • 20% loss ratio, lower hazard curve, less ALAE loading, combination of all three • Experience • LDF’s, claim counts, size of loss curve (industry or company) • what assumptions get result to exposure rate • 54 claims above 50k, heavier tail factor (1.238 @ 60 months to 2.2) • Assign weights to various outcomes and determine a new expected loss estimate • Credibility

  15. Reconciliation of Estimates • Leads to stochastic applications • Need to assign probabilities to various assumptions/scenarios • Think about independence of variable • Address parameter/process risk • Results in better pricing for AAD considerations, swing plans, stop loss treaties, etc.

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