风险建模的反向灵敏度分析
Reverse Sensitivity Analysis for Risk Modelling
摘要：
我们考虑的问题，建模者进行灵敏度分析的模型组成的随机输入因素，相应的随机输出的兴趣，和基线概率测量。建模者试图理解模型（输入因子和输出的分布）在输出分布的压力下如何变化。具体来说，对于输出随机变量上的应力，我们推导出输出的唯一应力分布，该分布在Wasserstein距离中最接近基线输出的分布并且满足应力。我们进一步推导出应力模型，包括输入的应力分布，它可以从一组基线蒙特卡罗样本中以数值有效的方式计算，并在CRAN上的R包SWIM中实现。建议的反向敏感性分析框架是无模型的，并允许对输出的压力，如（a）均值和方差，（b）任何扭曲的风险度量，包括风险价值和预期不足，以及（c）期望效用类型的限制，从而使反向敏感性分析框架适用于风险模型。
英文摘要：
We consider the problem where a modeller conducts sensitivity analysis of a model consisting of random input factors, a corresponding random output of interest, and a baseline probability measure. The modeller seeks to understand how the model (the distribution of the input factors as well as the output) changes under a stress on the output's distribution. Specifically, for a stress on the output random variable, we derive the unique stressed distribution of the output that is closest in the Wasserstein distance to the baseline output's distribution and satisfies the stress. We further derive the stressed model, including the stressed distribution of the inputs, which can be calculated in a numerically efficient way from a set of baseline Monte Carlo samples and which is implemented in the R package SWIM on CRAN. The proposed reverse sensitivity analysis framework is model-free and allows for stresses on the output such as (a) the mean and variance, (b) any distortion risk measure including the Value-at-Risk and Expected-Shortfall, and (c) expected utility type constraints, thus making the reverse sensitivity analysis framework suitable for risk models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
