Risk measures and insurance premium principles. (English) Zbl 1055.91053
Summary: Risk measures based on distorted probabilities have been recently developed in actuarial science and applied to insurance rate making. We propose a risk measure that has the properties of risk aversion and diversification, is additive for losses and consistent in its treatment of insurance and investment risks. We show that the risk measure based on distorted probabilities is not consistent in its ordering of insurance and investment risks.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
References:
| [2] | Gerber, H. U.; Pafumi, G., Utility functions: from risk theory to finance, North American Actuarial Journal, 2, 3, 74-100 (1998) · Zbl 1081.91511 |
| [7] | Sondermann, D., Reinsurance in arbitrage-free markets, Insurance: Mathematics and Economics, 10, 191-202 (1991) · Zbl 0739.62078 |
| [9] | Wang, S., Insurance pricing and increased limits rate-making by proportional hazard transforms, Insurance: Mathematics and Economics, 17, 43-54 (1995) · Zbl 0837.62088 |
| [10] | Wang, S., Premium Calculation by Transforming the Layer Premium Density, ASTIN Bulletin, 26, 71-92 (1996) |
| [11] | Wang, S., An actuarial index of right-tail risk, North American Actuarial Journal, 2, 2, 88-101 (1998) · Zbl 1081.62570 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
