论文标题
校准骨膜的分布模型
Calibrating distribution models from PELVE
论文作者
论文摘要
价值风险（VAR）和预期的不足（ES）是银行和保险法规中最流行的风险措施。为了在两种调节风险度量之间进行桥接，最近提出了VAR-ES（PELVE）的概率等效水平，以将一定水平的VAR转换为ES的水平。对于给定的分布模型，计算骨的值很简单。在本文中，我们研究了骨膜校准的相反问题，也就是说，要找到一个产生给定骨的分布模型，该模型可以从数据或专家意见中获得。我们分别讨论给出一分，两点，N点和曲线约束的情况。在曲线约束最复杂的情况下，我们将校准问题转换为高级微分方程的问题。我们将模型校准技术应用于保险中使用的数据集的估计和模拟。我们通过提供一些有关单调性和收敛性的新结果来进一步研究PELVE的一些技术特性。
The Value-at-Risk (VaR) and the Expected Shortfall (ES) are the two most popular risk measures in banking and insurance regulation. To bridge between the two regulatory risk measures, the Probability Equivalent Level of VaR-ES (PELVE) was recently proposed to convert a level of VaR to that of ES. It is straightforward to compute the value of PELVE for a given distribution model. In this paper, we study the converse problem of PELVE calibration, that is, to find a distribution model that yields a given PELVE, which may either be obtained from data or from expert opinion. We discuss separately the cases when one-point, two-point, n-point and curve constraints are given. In the most complicated case of a curve constraint, we convert the calibration problem to that of an advanced differential equation. We apply the model calibration techniques to estimation and simulation for datasets used in insurance. We further study some technical properties of PELVE by offering a few new results on monotonicity and convergence.
