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Non-life insurance mathematics

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring. Insurance works because risk can be diversified away through size. The core idea of insurance is risk spread on many units

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Non-life insurance mathematics

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  1. Non-lifeinsurancemathematics Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring

  2. Insurance worksbecause risk can be diversifiedawaythroughsize • The coreideaofinsurance is risk spreadonmanyunits • Assumethat policy risks X1,…,XJarestochastically independent • Mean and variance for theportfolio total arethen which is averageexpectation and variance. Then • The coefficientofvariationapproaches 0 as J grows large (lawof large numbers) • Insurance risk can be diversifiedawaythroughsize • Insurance portfoliosare still not risk-freebecause • ofuncertainty in underlyingmodels • risks may be dependent

  3. Whygiveaway business? Insurance company 1 Insurance company2 Reinsurance company Result elements Insurance companyn-1 The balancesheet Insurance companyn Premium Income • Stable resultseveryyearmay be more importantthanmaximisingtheprofit • Re-insurance is a sourceofcapital • Insurance companies in earlyphases or in growthmaywish to buyprotection • Regulationmayresult in specificre-insurancecontractsbeingbeneficial • Re-insurance is a tool in risk management • The objective is maximisationofrisk-adjustedreturnoncapital Losses Loss ratio Costs

  4. PP: Select detaillevel PP: Reviewpotential risk drivers PP: Select groups for each risk driver PP: Select largeclaimsstrategy PP: identifypotentialinteractions PP: construct final model Price assessment

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