Mathematics of Quantitative Risk Management under Uncertainty

最近的经济危机促使人们重新审视数学在整个金融、尤其是风险管理中的作用。从这种反省过程中得到的最重要的教训是认识到，模型的最终用户和开发模型的数学家都需要更多地关注模型不确定性在风险衡量和管理中的作用。该项目的目的是开发必要的基本数学和实用工具，以促进模型不确定性下的风险管理。将受到特别关注的两个应用领域是交易对手信用风险(CCR)和有担保的保险产品。交易对手信用风险(CCR)是指由于场外衍生品合约的交易对手资信发生不利变化而造成损失的风险。雷曼兄弟违约和美国国际集团几近违约对金融体系造成的破坏，戏剧性地说明了它的重要性。CCR损失既取决于不良信用事件的发生时间(由信用风险因素驱动)，也取决于事件发生时合约组合的价值(由市场风险因素驱动)。金融机构往往有单独的市场风险和信用风险模型；然而，对这两种风险类型的联合建模带来了重大挑战，特别是相关性结构是模型不确定性的一个来源。鉴于市场和信用风险之间的相关性存在不确定性，研究将侧重于得出CCR的最坏情况和保守界限。现代人寿保险产品变得越来越复杂，提供大量担保，并依赖于许多不同的风险来源。人寿保险公司在其担保产品组合中将面临的风险包括市场风险(例如利率、股权)、死亡风险和与投保人行为相关的风险(例如过错)。对这一主题的研究将集中在两个方向。第一个将是投保人的最佳行为。其次，研究了保险公司的决策过程对投保人的影响。

The recent economic crisis has led to a re-examination of the role of mathematics in finance in general, and risk management in particular. A lesson of paramount importance from this process of introspection has been the realization that both end users of models and the mathematicians who develop models need to pay more attention to the role of model uncertainty in the measurement and management of risk. The purpose of this project is to develop the underlying mathematics and practical tools necessary to facilitate the management of risk under model uncertainty. Two areas of application that will receive particular focus are counterparty credit risk (CCR) and insurance products with guarantees. Counterparty credit risk (CCR) refers to the risk of a loss due to an adverse change in the creditworthiness of a counterparty to an over-the-counter derivative contract. Its importance was dramatically illustrated by the devastation caused to the financial system by the default of Lehman brothers and the near default of AIG. CCR losses depend on both the timing of the adverse credit event (driven by credit risk factors), as well as the value of the portfolio of contracts when the event occurs (driven by market risk factors). Financial institutions often have in place models for market risk and credit risk separately; however, the joint modelling of these two risk types presents significant challenges, and the dependence structure in particular is a source of model uncertainty. Research will focus on deriving worst-case scenarios and conservative bounds for CCR given the uncertainty regarding the dependence between market and credit risk. Modern life insurance products have become increasing complex, offering numerous guarantees, and depending on many disparate sources of risk. Included among the risks a life insurer will face on its portfolio of guaranteed products are market (e.g. interest rate, equity) risk, mortality risk, and the risk associated with policyholder behaviour (e.g. lapse). Research on this topic will focus on two directions. The first will be the optimal behaviour for policyholders. Secondly, the impact of the insurer's decision making process on the policyholder will be studied.