英文标题：
《Structure conditions under progressively added information》
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作者：
Tahir Choulli and Jun Deng
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最新提交年份：
2018
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英文摘要：
It has been understood that the \"local\" existence of the Markowitz\' optimal portfolio or the solution to the local-risk minimization problem is guaranteed by some specific mathematical structures on the underlying assets price processes known in the literature as \"{\\it Structure Conditions}\". In this paper, we consider a semi-martingale market model, and an arbitrary random time that is not adapted to the information flow of the market model. This random time may model the default time of a firm, the death time of an insured, or any the occurrence time of an event that might impact the market model somehow. By adding additional uncertainty to the market model, via this random time, the {\\it structures conditions} may fail and hence the Markowitz\'s optimal portfolio and other quadratic-optimal portfolios might fail to exist. Our aim is to investigate the impact of this random time on the structures conditions from different perspectives. Our analysis allows us to conclude that under some mild assumptions on the market model and the random time, these structures conditions will remain valid on the one hand. Furthermore, we provide two examples illustrating the importance of these assumptions. On the other hand, we describe the random time models for which these structure conditions are preserved for any market model. These results are elaborated separately for the two contexts of stopping with the random time and incorporating totally a specific class of random times respectively.
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中文摘要：
据了解，马科维茨最优投资组合的“局部”存在性或局部风险最小化问题的解决方案是由文献中称为“{\\It Structure Conditions}”的基础资产价格过程的某些特定数学结构所保证的。在本文中，我们考虑了一个半鞅市场模型，以及一个不适应市场模型信息流的任意随机时间。这种随机时间可以模拟一家公司的违约时间、被保险人的死亡时间，或者任何可能以某种方式影响市场模型的事件的发生时间。通过给市场模型增加额外的不确定性，通过这个随机时间，{\\it structures conditions}可能会失败，因此马科维茨最优投资组合和其他二次最优投资组合可能不存在。我们的目的是从不同的角度研究这种随机时间对结构条件的影响。我们的分析允许我们得出结论，在市场模型和随机时间的一些温和假设下，这些结构条件一方面仍然有效。此外，我们还提供了两个例子来说明这些假设的重要性。另一方面，我们描述了随机时间模型，对于任何市场模型，这些结构条件都保持不变。这些结果分别在随机时间停止和完全合并一类特定随机时间的两种情况下阐述。
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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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