英文标题：
《Exact fit of simple finite mixture models》
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作者：
Dirk Tasche
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最新提交年份：
2014
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英文摘要：
  How to forecast next year\'s portfolio-wide credit default rate based on last year\'s default observations and the current score distribution? A classical approach to this problem consists of fitting a mixture of the conditional score distributions observed last year to the current score distribution. This is a special (simple) case of a finite mixture model where the mixture components are fixed and only the weights of the components are estimated. The optimum weights provide a forecast of next year\'s portfolio-wide default rate. We point out that the maximum-likelihood (ML) approach to fitting the mixture distribution not only gives an optimum but even an exact fit if we allow the mixture components to vary but keep their density ratio fix. From this observation we can conclude that the standard default rate forecast based on last year\'s conditional default rates will always be located between last year\'s portfolio-wide default rate and the ML forecast for next year. As an application example, then cost quantification is discussed. We also discuss how the mixture model based estimation methods can be used to forecast total loss. This involves the reinterpretation of an individual classification problem as a collective quantification problem.
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中文摘要：
如何根据去年的违约观察和当前的分数分布预测明年的投资组合范围内的信用违约率？解决这个问题的经典方法是将去年观察到的条件分数分布与当前分数分布进行混合拟合。这是有限混合模型的一个特殊（简单）情况，其中混合组分是固定的，只估计组分的权重。最佳权重可以预测明年整个投资组合的违约率。我们指出，如果我们允许混合物成分变化，但保持其密度比不变，那么拟合混合物分布的最大似然（ML）方法不仅给出了最佳拟合，甚至给出了精确拟合。根据这一观察，我们可以得出结论，基于去年条件违约率的标准违约率预测将始终位于去年投资组合范围内的违约率和明年的ML预测之间。作为一个应用实例，讨论了成本量化。我们还讨论了如何使用基于混合模型的估计方法来预测总损失。这涉及将单个分类问题重新解释为集体量化问题。
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分类信息：

一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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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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