Statistical estimation of composite risk functionals and risk optimization problems
Statistical estimation of composite risk functionals and risk optimization problems
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复合风险函数的统计估计和风险优化问题
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. Ruszczynski
中科院分区：
文献类型：
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作者：
Darinka Dentcheva;S. Penev;A. Ruszczynski
我们讨论了在概率度量中可能是非线性的复合泛函的统计估计。我们的研究的动机是需要估计一致的风险度量，这在金融、保险和其他与不确定性和风险下的优化相关的领域变得越来越流行。我们建立了复合风险泛函的中心极限定理。进一步，我们讨论了以复合风险泛函为目标的优化问题的渐近行为，并建立了当使用风险泛函的估计时其最优值的中心极限公式。虽然数学结构适应了通常使用的连贯的风险衡量标准，但它们具有更一般的特征，可能具有独立的利益。
We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance, insurance, and other areas associated with optimization under uncertainty and risk. We establish central limit theorems for composite risk functionals. Furthermore, we discuss the asymptotic behavior of optimization problems whose objectives are composite risk functionals and we establish a central limit formula of their optimal values when an estimator of the risk functional is used. While the mathematical structures accommodate commonly used coherent measures of risk, they have more general character, which may be of independent interest.