Orderings of Risks and Their Actuarial Applications
In actuarial theory a risk is a random variable describing a claim size (a single claim size, or the total claim amount of one contract in one period, or the aggregate claim of a portfolio of contracts in one period, e.g.). In the present contribution a number of (well-known as well as new) ordering...
| Veröffentlicht in: | Lecture Notes-Monograph Series. - Institute of Mathematical Statistics, 1982. - 19(1991) vom: Jan., Seite 157-173 |
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| 1. Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1991
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| Zugriff auf das übergeordnete Werk: | Lecture Notes-Monograph Series |
| Schlagworte: | Actuarial risk Dangerousness of risks Risk theory Premium calculation Mathematics Economics Philosophy |
| Zusammenfassung: | In actuarial theory a risk is a random variable describing a claim size (a single claim size, or the total claim amount of one contract in one period, or the aggregate claim of a portfolio of contracts in one period, e.g.). In the present contribution a number of (well-known as well as new) orderings of random variables are discussed. In particular, the relations between these orderings are investigated, and interpretations in terms of actuarial applications are given. Furthermore, the stability of the orderings with respect to convolutions and the forming of random sums is examined. Finally, it is shown that this approach can be used to generate formulas for risk premiums. |
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| ISSN: | 07492170 |