Concentration inequality of sums of dependent subexponential random variables and application to bounds for value-at-risk
Concentration inequality of sums of dependent subexponential random variables and application to bounds for value-at-risk
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因次指数随机变量之和的浓度不等式及其在风险值界限中的应用
DOI：
10.1080/03610926.2022.2150822
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Tanoue Yuta
中科院分区：
文献类型：
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作者：
西野涼子;中田泰子;永井由佳里;酒井一輔;酒井一輔;酒井一輔;酒井一輔;Tanoue Yuta
集中度不等式在高维统计、机器学习、优化、信号处理、时间序列分析和金融等领域有着广泛的应用。因此，迄今为止已经推导出了各种类型的浓度不等式。在这项研究中，我们得到了新的浓度不等式的次指数随机变量的和。第一个是具有部分相依结构的次指数随机变量和的集中不等式。第二类是Pearson的集中度不等式，将所得的集中度不等式应用于投资组合风险管理问题，得到了金融投资组合风险价值的上界。
Concentration inequalities are widely used tools in many fields such as high-dimensional statistics, machine learning, optimization, signal processing, time series analysis, and finance. Therefore, various types of concentration inequalities have been derived so far. In this study, we derived new concentration inequalities for the sum of subexponential random variables. First one is the concentration inequalities for the sum of subexponential random variables with partial dependence structure. Second one is the concentration inequalities with Pearson’sBy applying obtained concentration inequalities to the problem of portfolio risk management, we obtained upper bound for the value-at-risk of financial portfolio.