论文标题
基于Wasserstein距离估算凸风险功能的参数方法
A parametric approach to the estimation of convex risk functionals based on Wasserstein distance
论文作者
论文摘要
在本文中，我们探讨了在数学金融和精算科学背景下评估风险的静态环境，该背景考虑了可能无限维风险因素的分布中的模型不确定性。我们允许通过Wasserstein距离测量的基线模型周围进行扰动，并研究了可以参数化这种形式的概率不精确的程度。目的是提出一个凸风险功能，该功能在非参数不确定性方面包含了六个余量，并且仍然可以通过参数化模型近似。参数化的特定形式使我们能够基于神经网络开发一种数值方法，该方法既给出了风险功能的值和参考度量的最佳扰动。此外，我们研究了有关扰动的其他限制，即均值和the骨约束。我们表明，在这两种情况下，在损失函数的适当条件下，仍然可以通过传递到扰动模型的参数家族来估计风险功能，这再次允许通过神经网络进行数值近似。
In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor. We allow for perturbations around a baseline model, measured via Wasserstein distance, and we investigate to which extent this form of probabilistic imprecision can be parametrized. The aim is to come up with a convex risk functional that incorporates a sefety margin with respect to nonparametric uncertainty and still can be approximated through parametrized models. The particular form of the parametrization allows us to develop a numerical method, based on neural networks, which gives both the value of the risk functional and the optimal perturbation of the reference measure. Moreover, we study the problem under additional constraints on the perturbations, namely, a mean and a martingale constraint. We show that, in both cases, under suitable conditions on the loss function, it is still possible to estimate the risk functional by passing to a parametric family of perturbed models, which again allows for a numerical approximation via neural networks.
