华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (6): 146-155.

• 应用数学与基础数学 • 上一篇    下一篇

一类公理化资本分配法和广义加权分配法的应用

胡凤霞， 姚定俊   

  1. 华东师范大学 金融与统计学院, 上海 200241
  • 收稿日期:2009-12-01 修回日期:2010-03-01 出版日期:2010-11-25 发布日期:2010-11-25
  • 通讯作者: 胡凤霞

Applications of axiomatic capital allocation and generalized weighted allocation

HU Feng-xia, YAO Ding-jun   

  1. School of Finance and Statistics, East China Normal University, Shanghai 200241, China
  • Received:2009-12-01 Revised:2010-03-01 Online:2010-11-25 Published:2010-11-25
  • Contact: HU Feng-xia

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摘要： 研究了两种资本分配法的若干应用: 一种是已知的公理化法, 另一种是广义加权法. 首先列出了几种常见的风险测度, 运用公理化分配法, 给出了关于这些风险测度的分配公式. 并且就一个具体的模型, 计算了它的分配结果. 其次将已知的加权分配法扩展到广义加权分配法, 主要讨论了广义加权分配法在两个不同总风险下分配量的比较方法, 此方法源于资本分配的一个必备要求：单个风险的资本分配量不超过其原有风险资本. 最后给出了具体特例.

关键词: 资本分配, 风险测度, 方向导数, 条件期望, 资本分配, 风险测度, 方向导数, 条件期望

Abstract: Applications of two kinds of capital allocation principles were studied: one was axiomatic allocation which had been known, and the other was generalized weighted allocation. Firstly, several known risk measures were listed. Based on a axiomatic method, allocation formulae with respect to these risk measures were given. Then in view of a specific numerical model, its allocation results were calculated. Secondly, generalized weighted allocation, which was an extension of weighted allocation, was considered. A method for comparing the amounts of generalized weighted capital allocations under two different aggregate losses, which stems from diversifying property, was mainly discussed. And some special examples were given.

Key words: risk measure, directional derivative, conditional expectation, capital allocation, risk measure, directional derivative, conditional expectation

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