英文标题：
《Existence, uniqueness and stability of optimal portfolios of eligible
assets》
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作者：
Michel Baes, Pablo Koch-Medina, Cosimo Munari
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最新提交年份：
2017
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英文摘要：
In a capital adequacy framework, risk measures are used to determine the minimal amount of capital that a financial institution has to raise and invest in a portfolio of pre-specified eligible assets in order to pass a given capital adequacy test. From a capital efficiency perspective, it is important to identify the set of portfolios of eligible assets that allow to pass the test by raising the least amount of capital. We study the existence and uniqueness of such optimal portfolios as well as their sensitivity to changes in the underlying capital position. This naturally leads to investigating the continuity properties of the set-valued map associating to each capital position the corresponding set of optimal portfolios. We pay special attention to lower semicontinuity, which is the key continuity property from a financial perspective. This \"stability\" property is always satisfied if the test is based on a polyhedral risk measure but it generally fails once we depart from polyhedrality even when the reference risk measure is convex. However, lower semicontinuity can be often achieved if one if one is willing to focuses on portfolios that are close to being optimal. Besides capital adequacy, our results have a variety of natural applications to pricing, hedging, and capital allocation problems.
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中文摘要：
在资本充足率框架中，风险度量用于确定金融机构为通过给定的资本充足率测试而必须筹集和投资于预先指定的合格资产组合的最低资本额。从资本效率的角度来看，重要的是要确定一组合格资产的组合，这些资产可以通过筹集最少的资本来通过测试。我们研究了这种最优投资组合的存在性和唯一性，以及它们对基础资本状况变化的敏感性。这自然会导致研究集值映射的连续性属性，该映射与每个资本头寸以及相应的最优投资组合集相关联。我们特别关注下半连续性，这是从财务角度来看的关键连续性。如果测试基于多面体风险度量，则始终满足此“稳定性”属性，但一旦我们离开多面体，即使参考风险度量是凸的，它通常也会失败。然而，如果一个人愿意专注于接近最优的投资组合，通常可以实现较低的半连续性。除了资本充足率，我们的结果对定价、对冲和资本配置问题也有各种自然的应用。
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分类信息：

一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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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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