Fast Simulation Methods for Risk Management

计算机模拟广泛应用于风险的测量和管理。 该项目的目标是开发风险管理的快速模拟方法，重点是三个具体问题： (1)风险价值的估计和市场价格变化引起的风险的相关措施;（2）投资组合信用风险的估计;（3）破产概率和保险风险的估计。 这些问题中的每一个都提出了计算挑战，至少部分是因为它涉及稀有事件模拟的各个方面。 该项目旨在主要根据重要性抽样，开发减少差异的技术，专门针对每种情况下的主要困难来源。 从方法论的角度来看，研究的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）这些应用中使用的模型通常涉及风险源之间的复杂依赖关系，这使得方差缩减技术的开发变得过于复杂。 这两个问题在实践中至关重要，因为风险管理必然涉及尾部事件以及风险扩散降低风险的程度。健全的风险管理对国家金融体系的稳定至关重要。然而，企业有时将其视为遵守规章的成本，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。 美国目前在为金融服务业开发定量方法方面处于世界领先地位。 它的成功主要依赖于它的教育基础和训练有素的个人的供应。 哥伦比亚大学靠近世界主要金融中心之一，因此特别有能力成为该领域研究和教育的领导者。这个项目是哥伦比亚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.