Insurance design and tail risk management

由于市场环境的变化，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。该研究的重点是建立优化问题，以解决保险市场参与者的关注，开发风险管理的定量方法，并为市场参与者提供科学支持，使用保险政策和风险措施，以有效地管理风险。本研究将涉及两个主题领域：（A）保险供给和需求分析。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个别政策的优化问题，而提供了有限的讨论，在市场层面上，复杂的相互作用的参与者或风险的挑战，现有的方法。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，并揭示可能的不匹配。具体而言，我们将引入行为理论来描述由于信息获取的限制而导致的参与者的非完美理性，用博弈论来描述具有不同信息集的参与者之间的保单协商，并引入系统风险来刻画和控制风险之间的依赖性。 (B)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经成为风险评估和监管资本计算的标准。经典的保险理论依赖于分散化和风险汇集效应。然而，由于大规模损失事件的发生和风险之间的依赖性，特别是尾部风险，现代市场及其参与者变得更加脆弱。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策略。为此，我们将进一步扩展尾部风险措施及其应用的研究，尾部依赖的风险组合的特征，并调查（再）保险在保险公司的尾部风险管理的有效性。利用风险分担技术和风险测度的性质，研究了风险总量的基本量的界。 冲击加拿大在精算科学方面拥有国际领先的研究。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。研究生可以通过这项研究计划获得足够的培训，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.