英文标题：
《Kernel Based Estimation of Spectral Risk Measures》
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作者：
Suparna Biswas and Rituparna Sen
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最新提交年份：
2021
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英文摘要：
Spectral risk measures (SRMs) belong to the family of coherent risk measures. A natural estimator for the class of SRMs has the form of L-statistics. Various authors have studied and derived the asymptotic properties of the empirical estimator of SRM. We propose a kernel based estimator of SRM. We investigate the large sample properties of general L-statistics based on i.i.d and dependent observations and apply them to our estimator. We prove that it is strongly consistent and asymptotically normal. We compare the finite sample performance of our proposed kernel estimator with that of several existing estimators for different SRMs using Monte Carlo simulation. We observe that our proposed kernel estimator outperforms all the estimators. Based on our simulation study we have estimated the exponential SRM of four future indices-that is Nikkei 225, Dax, FTSE 100, and Hang Seng. We also perform a backtesting exercise of SRM.
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中文摘要：
光谱风险度量（SRM）属于一致风险度量的范畴。SRM类的自然估计具有L-统计量的形式。许多作者研究并推导了SRM经验估计的渐近性质。我们提出了一种基于核的SRM估计器。我们研究了基于i.i.d和相依观测的一般L-统计量的大样本性质，并将其应用于我们的估计。我们证明了它是强相合且渐近正态的。通过蒙特卡罗模拟，我们比较了我们提出的核估计器与几种现有估计器对不同SRM的有限样本性能。我们观察到，我们提出的核估计优于所有的估计。基于我们的模拟研究，我们估计了四个未来指数的指数SRM，即日经225指数、Dax指数、富时100指数和恒生指数。我们还对SRM进行了回溯测试。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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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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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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