英文标题：
《On the Fractal Geometry of the Balance Sheet and the Fractal Index of
  Insolvency Risk》
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作者：
A.K.M. Azhar, Vincent B.Y. Gan, W.A.T. Wan Abdullah, H. Zainuddin
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最新提交年份：
2015
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英文摘要：
  This paper reviews the economic and theoretical foundations of insolvency risk measurement and capital adequacy rules. The proposed new measure of insolvency risk is constructed by disentangling assets, debt and equity at the micro-prudential firm level. This new risk index is the Firm Insolvency Risk Index (FIRI) which is symmetrical, proportional and scale invariant. We demonstrate that the balance sheet can be shown to evolve with a fractal pattern. As such we construct a fractal index that can measure the risk of assets. This index can differentiate between the similarity and dissimilarity in asset risk, and it will also possess the properties of being self-similar and invariant to firm characteristics that make up its asset composition hence invariant to all types of risk derived from assets. Self-similarity and scale invariance across the cross section allows direct comparison of degrees of risk in assets. This is by comparing the risk dissimilarity of assets. Being naturally bounded to its highest upper bound, (0,2], the fractal index is able to serve like a risk thermometer. We assign geometric probabilities of insolvency P (equity is equal or less than 0 conditional on debt being greater than 0).
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中文摘要：
本文回顾了破产风险度量和资本充足率规则的经济学和理论基础。拟议中的破产风险新衡量标准是通过在微观审慎公司层面上分离资产、债务和股权来构建的。这种新的风险指数是企业破产风险指数（FIRI），它是对称的、成比例的和规模不变的。我们证明，资产负债表可以显示出分形模式的演变。因此，我们构建了一个可以衡量资产风险的分形指数。该指数可以区分资产风险的相似性和相异性，它还具有自相似性和对构成其资产构成的企业特征不变的特性，因此对资产衍生的所有类型的风险都是不变的。横截面上的自相似性和尺度不变性允许直接比较资产中的风险程度。这是通过比较资产的风险差异来实现的。由于分形指数自然地被限定在其最高上限（0,2），因此它能够像一个风险温度计一样发挥作用。我们将破产的几何概率P（如果债务大于0，则权益等于或小于0）。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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