This paper is concerned with the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). We recast the traditional Euler contributions from an expectation conditional on an event of zero probability to a ratio involving conditional expectations whose conditioning events have stricktly positive probability. We derive an analytical form of the proposed representation of VaR contributions for various parametric models. Our numerical experiments show that the estimator using this novel representation outperforms the standard Monte Carlo estimator in terms of bias and variance. Moreover, unlike the existing estimators, the proposed estimator is free from hyperparameters.

翻译：本文涉及在选择风险计量标准为风险值(VaR)时,通用多变量模型的风险分配过程。我们根据零概率事件和有条件预期比率(其条件性事件具有惊人的积极概率)对传统的 Euler 贡献值进行重新设定。我们对各种参数模型的VaR贡献值的拟议表示方式进行了分析。我们的数字实验表明,使用这种新型表示法的估算值在偏差和差异方面超过了Monte Carlo估计值的标准。此外,与现有的估计值不同的是,拟议的估计值没有超光度。