×
Goovaerts, Marc J.; Kaas, Rob; Dhaene, Jan; Tang Qihe

Some new classes of consistent risk measures. (English) Zbl 1188.91087

Insur. Math. Econ. 34, No. 3, 505-516 (2004).
Summary: Many types of insurance premium principles and/or risk measures can be characterized by means of a set of axioms, which in many cases are rather arbitrarily chosen and not always in accordance with economic reality. In the present paper we generalize Yaari’s risk measure by relaxing his axioms. In addition, we derive translation invariant minimal Orlicz risk measures, which we call Haezendonck risk measures, and obtain sufficient conditions on the risk measure of Bernoulli risks to fulfill additivity and superadditivity properties for Orlicz premium principles.

Cited in 4 Reviews
Cited in 48 Documents

MSC:

91B30 Risk theory, insurance (MSC2010)
60E05 Probability distributions: general theory
60E15 Inequalities; stochastic orderings
62E10 Characterization and structure theory of statistical distributions
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B82 Statistical methods; economic indices and measures

Keywords:

Consistent risk measures; Haezendonck risk measure; Monotone convergence theorem
PDF BibTeX XML Cite
\textit{M. J. Goovaerts} et al., Insur. Math. Econ. 34, No. 3, 505--516 (2004; Zbl 1188.91087)
Full Text: DOI Link
  • logo of hbz
  • logo of WorldCat

References:

[1] Bühlmann, H., 1970. Mathematical Methods in Risk Theory. Springer-Verlag, New York.
[2] Bühlmann, H.; Gagliardi, B.; Gerber, H.U.; Straub, E., Some inequalities for stop-loss premiums, Astin bulletin, 9, 1, 75-83, (1977)
[3] Dhaene, J.; Denuit, M.; Goovaerts, M.J.; Kaas, R.; Vyncke, D., The concept of comonotonicity in actuarial science and finance: theory, Insurance: mathematics and economics, 31, 1, 3-33, (2002) · Zbl 1051.62107
[4] Dhaene, J.; Denuit, M.; Goovaerts, M.J.; Kaas, R.; Vyncke, D., The concept of comonotonicity in actuarial science and finance: applications, Insurance: mathematics and economics, 31, 2, 133-161, (2002) · Zbl 1037.62107
[5] Gerber, H.U., 1979. An Introduction to Mathematical Risk Theory. University of Pennsylvania, Philadelphia. · Zbl 0431.62066
[6] Gerber, H.U., On additive principles of zero utility, Insurance: mathematics and economics, 4, 4, 249-251, (1985) · Zbl 0584.62172
[7] Goovaerts, M.J., De Vijlder, F., Haezendonck, J., 1984. Insurance Premiums. Theory and Applications. North-Holland, Amsterdam. · Zbl 0532.62082
[8] Goovaerts, M.J.; Kaas, R.; Dhaene, J., Economic capital allocation derived from risk measures, North American actuarial journal, 7, 2, 44-59, (2003) · Zbl 1084.91515
[9] Goovaerts, M.J.; Kaas, R.; Dhaene, J.; Tang, Q., A unified approach to generate risk measures, Astin bulletin, 33, 2, 173-191, (2003) · Zbl 1098.91539
[10] Haezendonck, J.; Goovaerts, M., A new premium calculation principle based on Orlicz norms, Insurance: mathematics and economics, 1, 1, 41-53, (1982) · Zbl 0495.62091
[11] Kaas, R., Goovaerts, M.J., Dhaene, J., Denuit, M., 2001. Modern Actuarial Risk Theory. Kluwer Academic Publishers, Dordrecht. · Zbl 1086.91035
[12] Wang, S.S., Premium calculation by transforming the layer premium density, Astin bulletin, 26, 1, 71-92, (1996)
[13] Wang, S.S.; Young, V.R., Ordering risks: expected utility theory versus yaari’s dual theory of risk, Insurance: mathematics and economics, 22, 2, 145-161, (1998) · Zbl 0907.90102
[14] Yaari, M.E., The dual theory of choice under risk, Econometrica, 55, 1, 95-115, (1987) · Zbl 0616.90005
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.