英文标题：
《Two maxentropic approaches to determine the probability density of
compound risk losses》
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作者：
Erika Gomes-Gon\\c{c}alves (UC3M), Henryk Gzyl (IESA) and Silvia
Mayoral (UC3M)
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最新提交年份：
2014
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英文摘要：
Here we present an application of two maxentropic procedures to determine the probability density distribution of compound sums of random variables, using only a finite number of empirically determined fractional moments. The two methods are the Standard method of Maximum Entropy (SME), and the method of Maximum Entropy in the Mean (MEM). We shall verify that the reconstructions obtained satisfy a variety of statistical quality criteria, and provide good estimations of VaR and TVaR, which are important measures for risk management purposes. We analyze the performance and robustness of these two procedures in several numerical examples, in which the frequency of losses is Poisson and the individual losses are lognormal random variables. As side product of the work, we obtain a rather accurate description of the density of the compound random variable. This is an extension of a previous application based on the Standard Maximum Entropy approach (SME) where the analytic form of the Laplace transform was available to a case in which only observed or simulated data is used. These approaches are also used to develop a procedure to determine the distribution of the individual losses through the knowledge of the total loss. Then, in the case of having only historical total losses, it is possible to decompound or disaggregate the random sums in its frequency/severity distributions, through a probabilistic inverse problem.
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中文摘要：
在这里，我们提出了一个应用两个最大熵过程来确定随机变量复合和的概率密度分布，只使用有限个经验确定的分数矩。这两种方法是标准的最大熵法（SME）和平均最大熵法（MEM）。我们将验证获得的重建满足各种统计质量标准，并提供VaR和TVaR的良好估计，这是风险管理的重要措施。我们在几个数值例子中分析了这两种方法的性能和鲁棒性，其中损失的频率是泊松分布，单个损失是对数正态随机变量。作为工作的副产品，我们得到了复合随机变量密度的一个相当精确的描述。这是之前基于标准最大熵方法（SME）的应用程序的扩展，其中拉普拉斯变换的分析形式适用于仅使用观测或模拟数据的情况。这些方法还用于开发一个程序，通过对总损失的了解来确定单个损失的分布。然后，在只有历史总损失的情况下，可以通过概率反问题分解或分解其频率/严重性分布中的随机和。
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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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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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