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Risk theory and its statistics enviroment. (English) Zbl 0697.62098

Summary: Modern risk theory is so comprehensive and its borderline so elastic that only selected parts of it can be treated in a brief survey. The present one centers on a few prominent branches related to insurance matters. Still they cover a variety of models and methods:
- Utility theoretical description of attitudes to risk. Ordering of risks, optimal insurance coverages, optimal risk exchanges.
- Modern life history analysis applied to life insurance and related coverages.
- Heterogeneity models applied to classification/tariffication of individual risks. Empirical (possibly restricted) Bayes estimators.
- Stochastic processes applied to ruin theory.
- Numerical methods for calculation of total claims distributions.
- Some special problems arising in insurance: incurred but not settled claims; assessment of the solvency of an insurer.
Emphasis is laid on current theoretical developments and interplay with general statistics.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
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