容度空间上保费泛函的Choquet积分表示及相关性质

J4 ›› 2013, Vol. 48 ›› Issue (1): 78-82.

容度空间上保费泛函的Choquet积分表示及相关性质

杨莹,江龙*,索新丽

中国矿业大学理学院, 江苏徐州 221116

收稿日期:2012-03-22 出版日期:2013-01-20 发布日期:2013-01-15
通讯作者: 江龙(1964- ),男, 教授, 博士生导师,研究方向为随机分析与金融数学. Email: jianglong365@cumt.edu.cn
作者简介:杨莹(1984- ),女, 硕士研究生, 研究方向为随机分析与金融数学. Email: yangyingcumt@163.com
基金资助:
国家自然科学基金资助项目(10971220);全国优秀博士学位论文作者专项基金资助项目(200919);中央高校基本科研业务费专项资金项目(2010LKSX04);江苏省“青蓝工程”基金资助项目

Choquet integral representation of premium functional and related properties on capacity space

YANG Ying, JIANG Long*, SUO Xin-li

College of Science, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

Received:2012-03-22 Online:2013-01-20 Published:2013-01-15

摘要/Abstract

摘要：

研究容度空间上的保费泛函,证明了满足分布单调性、共单调可加性与规范性的保费泛函可以表示成关于扭曲容度的Choquet积分,并给出了扭曲函数g的存在性与惟一性定理及扭曲容度的一些相关性质。

关键词: 保费泛函;Choquet积分;容度;容度空间

Abstract:

The premium functional on capacity space was investigated, and the results prove that the premium functional that satisfies monotonicity of the distribution, comonotonic additivity and normativity can be represented as Choquet integral with respect to the distorted capacity. And then the theorem of the existence and uniqueness of the distorted function g and some related properties of the distorted capacity were obtained.

Key words: premium functional; Choquet integral; capacity; capacity space

杨莹,江龙*,索新丽. 容度空间上保费泛函的Choquet积分表示及相关性质[J]. J4, 2013, 48(1): 78-82.

YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78-82.

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