Insurance design and tail risk management

由于市场条件的变化，现代保险市场面临着比以往更多的挑战，需要先进的概念和新颖的方法来研究复杂的市场参与者的行为，并制定先进的风险管理策略。本研究的重点是建立保险市场参与者关注的优化问题，发展风险管理的定量方法，为市场参与者利用保险政策和风险措施有效管理风险提供科学支持。本研究将涉及两个主题领域：(A)保险供需分析。在保险市场中，参与者使用（再）保险政策来有效地优化他们的个人观点。目前的研究主要集中在单个政策的优化问题上，而在市场层面上的讨论有限，其中参与者之间复杂的相互作用或风险对现有方法提出了挑战。我们的目标是使用三套先进的数学和经济工具来建立和解决市场层面的优化问题。我们将分析整个市场的保险需求和供给，并揭示可能出现的错配。准确地说，我们将把行为理论引入到由于信息获取的限制而导致的参与者的不完全理性的制定中，用博弈论来描述具有不同信息集的参与者之间的保险单谈判，并引入系统风险来表征和控制风险之间的依赖关系。（二）尾部风险管理。在银行和保险监管中，衡量风险的尾部行为已成为风险评估和监管资本计算的标准。传统的保险理论依赖于多元化和风险汇集效应。然而，由于大规模损失事件的发生以及风险之间的依赖性，现代市场及其参与者变得更加脆弱，特别是在尾部。因此，有必要量化尾部的风险行为，并进一步制定有效的风险缓解战略。为此，我们将进一步扩展尾部风险度量及其应用的研究，描述风险组合的尾部依赖性，并研究（再）保险在保险公司尾部风险管理中的有效性。本文将运用风险分担技术和风险测度的性质来研究总风险的基本量的界限。的影响。加拿大在精算科学方面的研究处于国际领先地位。拟议的研究有助于更好地了解加拿大保险市场现有的挑战，并获得克服这些问题的创新技术。研究生可以通过这个研究项目获得足够的训练，以支持他们未来在学术界和保险业的职业生涯。

Modern insurance markets are facing more challenges than before due to changes in market conditions, and are calling for advanced concepts and novel methodologies to study sophisticated market participants' behaviours and to develop advanced risk management strategies. The proposed research focuses on establishing optimization problems to address concerns for insurance market participants, developing quantitative methodologies in risk management, and providing market participants scientific support on using insurance policies and risk measures to efficiently manage risks. This research will address two theme areas: (A) Analysis of insurance supply and demand. In insurance markets, participants use (re)insurance policies to effectively optimize their personal perspectives. Current research mainly focuses on optimization problems for individual policies, while provides limited discussion at the market level, in which complicated interplay among participants or risks challenges the existing methodologies. We aim at using three sets of advanced mathematical and economic tools to establish and to solve optimization problems at the market level. We will analyze insurance demand and supply for the entire market, and reveal the possible mismatch. Precisely, we will bring the behaviour theory in the formulation of nonperfect rationalities for participants due to the limitation on acquiring information, use game theory to describe the negotiation of the insurance policies among participants with different sets of information, and introduce systematic risk to characterize and to control the dependence among risks. (B) Tail risk management. In banking and insurance regulations, measuring tail behaviour of risks has become a standard assessment for risks and regulatory capital calculation. Classical insurance theories rely on the diversification and the risk pooling effect. However, modern markets and participants therein have become more vulnerable due to the occurrence of large-scale loss events and the dependence among risks, especially in the tails. Therefore, it is necessary to quantify risk behaviours in the tail and further develop effective risk mitigation strategies. To this end, we will further extend the study of tail risk measures and their applications, characterize tail dependence for a portfolio of risks, and investigate the effectiveness of (re)insurance in an insurer's tail risk management. Technique on risk sharing and properties of risk measures will be used to study bounds on essential quantities of the aggregate risks. Impact. Canada has internationally leading research in actuarial science. The proposed research helps to understand existing challenges in Canadian insurance markets better and to gain innovative techniques on overcoming those problems. Graduate students can obtain sufficient training through this research program to support their future career in both academia and insurance industry.