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On Haezendonck risk measures

机译:关于Haezendonck的风险衡量

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We study the Haezendonck risk measure (introduced by Haezendonck, J., Goovaerts, M., 1982. A new premium calculation principle based on Orlicz norms. Insurance: Mathematics and Economics 1, 41-53 and by Goovaerts, M.J., Kaas, R., Dhaene, J., Tang, Q., 2003. A unified approach to generate risk measures. ASTIN Bulletin 33 (2), 173-191; Goovaerts, M.J., Kaas, R., Dhaene, J., Tang, Q., 2004. Some new classes of consistent risk measures. Insurance: Mathematics and Economics 34 (3), 505-516) and prove its subadditivity. Since the Haezendonck risk measure is defined as an infimum of Orlicz premia, we investigate when the infimum is actually attained. We determine the corresponding generalized scenarios and show how its construction can be seen as a special case of the operation of inf-con-volution of convex functionals.
机译:我们研究了Haezendonck风险度量(由Haezendonck,J.,Goovaerts,M.于1982年提出。一种基于Orlicz准则的新保费计算原理。保险:数学与经济学1,41-53,以及Goovaerts,MJ,Kaas,R 。,Dhaene,J.,Tang,Q.,2003.一种生成风险度量的统一方法。ASTIN公告33(2),173-191; Goovaerts,MJ,Kaas,R.,Dhaene,J.,Tang,Q ,2004年。一些新类别的一致风险度量,保险:数学和经济学34(3),505-516)并证明了其次可加性。由于Haezendonck风险量度被定义为Orlicz溢价的最低限度,因此我们将调查何时实际达到最低限度。我们确定相应的广义方案,并说明如何将其构造视为凸泛函的inf-卷积运算的特例。

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