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 Assume that policy risks X 1,…,X J are stochastically independent Mean and variance for the portfolio total are then which is average expectation and variance. Then The coefficient of variation approaches 0 as J grows large (law of large numbers) Insurance risk can be diversified away through size Insurance portfolios are still not risk-free because of uncertainty in underlying models risks may be dependent

The balance sheet Premium Income Losses Loss ratio Costs Result elements Why give away business? 3 Insurance company 1 Reinsurance company Insurance company 2 Insurance company n- 1 Insurance company n Stable results every year may be more important than maximising the profit Re-insurance is a source of capital Insurance companies in early phases or in growth may wish to buy protection Regulation may result in specific re-insurance contracts being beneficial Re-insurance is a tool in risk management The objective is maximisation of risk-adjusted return on capital

PP: Select detail level PP: Review potential risk drivers PP: Select groups for each risk driver PP: Select large claims strategy Price assessment PP: identify potential interactions PP: construct final model