Fast Simulation Methods for Risk Management

计算机模拟被广泛应用于风险的度量和管理。该项目的目标是开发风险管理的快速模拟方法，重点关注三个具体问题：(1)估计风险价值和市场价格变化引起的风险的相关度量；(2)组合信用风险估计；(3)破产概率和保险风险的估计。这些问题中的每一个都带来了计算上的挑战，至少在一定程度上是因为它涉及到罕见事件模拟的各个方面。本项目旨在开发主要基于重要性抽样的减少差异技术，专门用于解决每种情况下困难的主要来源。从方法论的角度来看，研究挑战主要在于两个问题：(a)这些应用通常需要开发适合于传统罕见事件模拟方法不适用的重尾分布的方法；(b)在这些应用中使用的模型通常涉及风险来源之间复杂的依赖关系，这也使方差减少技术的发展复杂化。这两个问题在实践中都是至关重要的，因为风险管理必然涉及尾部事件，以及分散风险降低风险的程度。健全的风险管理对国家金融体系的稳定至关重要。然而，公司有时将其视为遵守法规的成本，而不是竞争优势的来源，因此在开发必要工具方面投资不足。受资助的学术研究在推进风险管理方法方面发挥着重要作用。在为金融服务业开发量化方法方面，美国目前处于世界领先地位。它的成功主要依赖于它的教育基础和训练有素的人才。哥伦比亚大学毗邻世界主要金融中心之一，在这一领域的研究和教育方面处于领先地位。这个项目是哥伦比亚大学研究和教育活动网络的一部分。除了支持pi的研究外，它还将支持博士生并促进与工业界的研究互动。

Computer simulation is widely used in measuring and managing risk. The objective of this project is to develop fast simulation methods for risk management, focusing on three specific problems: (1) estimation of value-at-risk and related measures of the risks resulting from changes in market prices; (2) estimation of portfolio credit risk; and (3) estimation of ruin probabilities and insurance risk. Each of these problems poses a computational challenge at least in part because it involves aspects of rare event simulation. This project seeks to develop variance reduction techniques, based primarily on importance sampling, specifically designed to address the key sources of difficulty in each case. From a methodological perspective, the research challenge lies primarily in two issues: (a) these applications often require developing methods suitable for heavy-tailed distributions to which traditional rare event simulation methods are inapplicable; (b) the models used in these applications often involve complex dependence between sources of risk, and this too complicates the development of variance reduction techniques. Both issues are of central importance in practice because risk management is necessarily concerned with tail events and with the extent to which spreading risk reduces risk.Sound risk management is essential to the stability of the nation's financial system. Yet firms sometimes view it as a cost of complying with regulations rather than as a source of competitive advantage and therefore underinvest in developing the necessary tools. Funded academic research has an important role to play in advancing risk management methods. The US is currently a world leader in developing quantitative methods for the financial services industry. Its success relies primarily on its educational base and supply of highly trained individuals. With its proximity to one of the world's major financial centers, Columbia University is particularly well positioned to be a leader in research and education in this area. This project is part of a network of research and educational activities at Columbia. In addition to supporting the PIs' research it will support doctoral students and foster research interactions with industry.