英文标题：
《Weak comonotonicity》
---
作者：
Ruodu Wang, Ricardas Zitikis
---
最新提交年份：
2019
---
英文摘要：
  The classical notion of comonotonicity has played a pivotal role when solving diverse problems in economics, finance, and insurance. In various practical problems, however, this notion of extreme positive dependence structure is overly restrictive and sometimes unrealistic. In the present paper, we put forward a notion of weak comonotonicity, which contains the classical notion of comonotonicity as a special case, and gives rise to necessary and sufficient conditions for a number of optimization problems, such as those arising in portfolio diversification, risk aggregation, and premium calculation. In particular, we show that a combination of weak comonotonicity and weak antimonotonicity with respect to some choices of measures is sufficient for the maximization of Value-at-Risk aggregation, and weak comonotonicity is necessary and sufficient for the Expected Shortfall aggregation. Finally, with the help of weak comonotonicity acting as an intermediate notion of dependence between the extreme cases of no dependence and strong comonotonicity, we give a natural solution to a risk-sharing problem.
---
中文摘要：
在解决经济、金融和保险领域的各种问题时，共名的经典概念发挥了关键作用。然而，在各种实际问题中，这种极端正依赖结构的概念过于严格，有时甚至不切实际。在本文中，我们提出了弱共单调性的概念，其中包含了经典的共单调性概念作为特例，并给出了一些优化问题的充要条件，如投资组合多样化、风险聚合和溢价计算中出现的问题。特别是，我们表明，对于某些度量选择，弱共单调性和弱反单调性的组合足以实现风险价值加总的最大化，而弱共单调性对于预期短缺加总是必要和充分的。最后，借助于弱共单调性作为无依赖和强共单调性极端情况之间依赖的中间概念，我们给出了一个风险分担问题的自然解。
---
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
--

---
PDF下载：
-->