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Risk Management EABH & Swiss Re

Risk Management EABH & Swiss Re. Mathematics at Swiss Re in the 1960s Hans Bühlmann June 2013. 1. Mathematics in insurance / Actuaries. Actuaries of the first kind ~ 18th century Life insurance Individual Risk Theory each policy bottom up

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Risk Management EABH & Swiss Re

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  1. Risk ManagementEABH & Swiss Re Mathematics at Swiss Re in the 1960s Hans Bühlmann June 2013

  2. 1. Mathematics in insurance / Actuaries Actuaries of the first kind ~ 18th century Life insurance Individual RiskTheoryeachpolicy bottomup Cash Flow Accounting: EQUIVALENCE PRINCIPLE Present Value Matching interestrates mortality All this: In a DeterministicModel ! Law of Large Numbers

  3. 1. Mathematics in insurance / Actuaries Actuaries of the second kind ~ middleof 20th century All Branchesof Insurance + Total of Insurance Company Collective RiskTheory total topdown Swiss Re decision in 1961 Witnessofthispioneeringperiod Riskmanagementwithoutcallingit so 2 concreteexamplestogetinsightintothethenactivity

  4. 2. Rating of Excess of Loss Reinsurance Treaties (XL-Treaties) History of XL-Treaty last five years For covered portfolio ceding company has earned premium T = 10mio XL Treaty with limit 100 000 (retention) …. …. …. B

  5. 2. Rating of Excess of Loss Reinsurance Treaties (XL-Treaties) B is called Burning Cost Burning Cost in percent : 13.35% of total premium T Burning Cost Rate What premium should we change for next years? First Idea Premium = B% . T next year Underwriter Premium = B% . T next year Actuary Premium = (B% + α F%) T next year B% 100 ______________________ 75

  6. 2. Rating of Excess of Loss Reinsurance Treaties (XL-Treaties) F% ~ fluctuationmeasureofdata % e.g. standarddeviation α ~ chosen such that total of all XL-treatiesisproducing a losswithsmallprobability Generally:Actuaryproducesclassof Premium CalculationPrinciples. Choice byconsiderationof total businessofreinsurer => topdown

  7. 3. How to Choose the Retention Limit Also Swiss Re cannot run arbitrarily high engagements SR buys reinsurance on reinsurance business retrocession How should Swiss Re fix its retention under retrocession treaties?

  8. 3. How to Choose the Retention Limit Actuarial method (Bruno De Finetti 1940) a) Relative Retentions (Retention) Branchiί = C αί αί~ ProfitabilityBranchί Limit in XL MPL in proportional reinsurance Historical remark: H. Markowitz, 1952

  9. 3. How to Choose the Retention Limit b) Absolute retention Fix the constant C in a) ί) Chooseoperative capital buffertoabsorblosses bufferwhichyouarewillingtoloose buffer ? - such that the company can survive - such that the company can digest it on its balance sheet - full surplus

  10. 3. How to Choose the Retention Limit ίί) Chooseacceptableprobabilityofloosingthebuffer - longterm => Cramér-Lundberg formula: probabilityofruin - shortterm : probabilityofdefault operative capital Ψ (u) = e-ku prob. ruindepends on riskportfolio retentionlimits on theconstant C

  11. Conclusion • Probability of ruin enters into formula for Con logarithmic scale • Operative capital and profitability are the main drivers:C depends linearly on k and u

  12. Interesting for today • Questions of solvency • Attitude towards risk: - Security- Profitability

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