Modeling and Optimization of Risk Measures

风险措施的建模和优化

• 批准号: RGPIN-2014-05602
• 负责人: Li, Jonathan
• 金额: $ 1.6万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=657457
• 关键词: Modeling; Optimization; Risk; Measures

Stunning financial losses have been witnessed in recent years due to risk underestimation. The management of pension funds is one of the many examples, where the failure of measuring the actual risk involved has led to widespread economic instability. This raises a pressing need to design new risk measures that capture risk overlooked by existing measures. Off-the-shelf measures such as Value-at-Risk (VaR) generate numerical risk estimates by assuming that all uncertainty can be represented by a probability distribution, and the rest is just a statistical exercise. The real world however, as evidenced by the 2008 financial crisis, is far more uncertain than what a distribution can describe. This multifaceted uncertainty has now gradually learned by decision makers, but a risk measure that embodies this knowledge is still lacking. **More sophisticated measures have been proposed lately. In the area of Robust Optimization (RO), a series of works have been done to design robust measures that allow the use of multiple distributions to describe uncertainty. Meanwhile, in Risk Analysis, axioms have been introduced that define the properties of ideal risk measures. While these works provide a whole new spectrum of measures, they leave the following question open: Which one of them accounts precisely for the actual uncertainty and risk facing decision makers?**Modern risk analysis theory does not provide a definite answer to this - largely because there is no single measure that can fit all situations. Decision makers from different sectors or industries can have different perspectives of risk, depending on the nature of the work undertaken. Current models of risk measures provide only narrow views of risk and are not amenable to incorporating decision makers' knowledge of risk. This gap between what current models offer and what decision makers need to measure is one of the greatest impediments toward the widespread deployment of risk measures. **The goal of this research program is to close the gap by developing a new interactive scheme that allows decision makers' knowledge of risk to be explored and incorporated into the design of risk measures. This scheme shares the same spirit as Interactive Optimization (IO), where the solution procedure involves user input in seeking preferable solutions. Important research questions to ask while developing this scheme include:*- How should we interact with users to best elicit their knowledge of risk?*- How can this information be incorporated into the design of risk measures?*- How can we provide guarantees on the quality of risk estimates even if only limited resource is available for elicitation? *- How can we ensure, given enough resource for elicitation, that the resulting risk measure converges to the one that best represents a user's knowledge of risk?*- How can the resulting measures be integrated into a decision optimization process?**Our methodology will be developed based on three streams of research: Robust Optimization, axiomatic approaches in Risk Analysis, and Interactive Optimization, which if successfully developed will also provide theoretical evidence of how these approaches can be integrated in the context of risk analytics. The end result of this research program will be a new decision support system that enables decision makers to model their knowledge of risk and to minimize them. The system will be validated using case studies from the sectors of finance, energy, and health care. This will bridge the gap between theory and practice in risk analytics, and encourage practitioners to approach risk management problems analytically, which is critically important in today's ever-changing environment.

由于对风险的低估，近年来出现了惊人的经济损失。养老基金的管理就是众多例子之一，在这些例子中，未能衡量所涉及的实际风险导致了广泛的经济不稳定。这就迫切需要设计新的风险度量来捕捉现有度量所忽略的风险。诸如风险价值（VaR）等现成的度量方法通过假设所有的不确定性都可以用概率分布来表示，从而产生数字风险估计，其余的只是统计练习。然而，正如2008年金融危机所证明的那样，现实世界的不确定性远远超出了一个分布所能描述的范围。决策者现在已经逐渐了解了这种多方面的不确定性，但仍然缺乏体现这种知识的风险度量。最近提出了更复杂的措施。在鲁棒优化（RO）领域，已经完成了一系列工作来设计允许使用多个分布来描述不确定性的鲁棒度量。同时，在风险分析中，引入了定义理想风险测度性质的公理。虽然这些工作提供了一个全新的测量范围，但它们留下了以下问题：它们中的哪一个准确地解释了决策者面临的实际不确定性和风险？**现代风险分析理论并没有对此提供一个明确的答案——很大程度上是因为没有一种单一的措施可以适用于所有的情况。根据所从事工作的性质，来自不同部门或行业的决策者可能对风险有不同的看法。目前的风险度量模型只提供了狭隘的风险观点，并且不适合纳入决策者的风险知识。当前模型提供的和决策者需要度量的之间的差距是风险度量广泛部署的最大障碍之一。**本研究计划的目标是通过开发一种新的互动方案来缩小差距，该方案允许决策者探索风险知识并将其纳入风险措施的设计中。该方案与交互优化（IO）具有相同的精神，其中解决过程涉及用户输入以寻求更优的解决方案。在开发此方案时需要提出的重要研究问题包括：*-我们应该如何与用户互动以最好地获取他们对风险的了解？*-如何将这些信息纳入风险措施的设计？*-在资源有限的情况下，我们如何保证风险评估的质量？*-在有足够的资源进行启发的情况下，我们如何确保最终的风险度量趋同于最能代表用户风险知识的度量？*-如何将测量结果整合到决策优化过程中？**我们的方法将基于三个研究流：鲁棒优化、风险分析中的公理方法和交互式优化，如果成功开发，也将为如何将这些方法集成到风险分析的背景下提供理论证据。这项研究计划的最终结果将是一个新的决策支持系统，使决策者能够模拟他们的风险知识并将其最小化。该系统将通过金融、能源和卫生保健部门的案例研究进行验证。这将弥合风险分析理论与实践之间的差距，并鼓励从业者分析地处理风险管理问题，这在当今不断变化的环境中至关重要。