A family of premium principles based on mixtures of TVaRs |
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| Institution: | 1. Department of Mathematics, Jinan University, Guangzhou, 510630, PR China;2. Department of Statistics, Jinan University, Guangzhou, 510630, PR China;3. Department of Mathematics, National Tsing Hua University, Hsinchu 30013, Taiwan;1. Department of Wealth and Taxation Management, National Kaohsiung University of Applied Sciences, No. 415, Chien-Kung Rd., Sanmin District, Kaohsiung City 80778, Taiwan;2. Department of Banking and Finance, National Chiayi University, No. 80, Sinmin Road, Chiayi City 60054, Taiwan;1. Department of Statistics, Miami University, 319 Upham Hall, 100 Bishop Circle, Oxford, OH 45056-1879, United States;2. Department of Applied Statistics, Johannes Kepler Universität Linz, Altenbergerstraße 69, 4040 Linz, Austria;1. Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada;2. Department of Statistics, Purdue University, West Lafayette, IN 47906, USA |
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| Abstract: | Risk-adjusted distributions are commonly used in actuarial science to define premium principles. In this paper, we claim that an appropriate risk-adjusted distribution, besides satisfying other desirable properties, should be well-behaved under conditioning with respect to the original risk distribution. Based on a sequence of such risk-adjusted distributions, we introduce a family of premium principles that gradually incorporate the degree of risk-aversion of the insurer in the risk loading. Members of this family are particular distortion premium principles that can be represented as mixtures of TVaRs, where the weights in the mixture reflect the attitude toward risk of the insurer. We make a systematic study of this family of premium principles. |
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| Keywords: | Tail value-at-risk Premium principle Risk measure Order statistics Distortion function |
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