Risk measures in portfolio selection and optimal reinsurance

投资组合选择和最佳再保险中的风险衡量

• 批准号: RGPIN-2020-07013
• 负责人: Wei, Pengyu
• 金额: $ 1.31万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=718642
• 关键词: Risk; measures; portfolio; selection; optimal

Risk and uncertainty are the indispensable nature of the financial and insurance markets. Financial mathematicians and actuaries use risk measures to quantify the risk. The risk measures we use have evolved from qualitative descriptions to a more quantitatively measuring of risk. Abundant research has been carried out to study the statistical property of various risk measures but little is known about how these risk measures can affect risk management decisions in financial and insurance institutions. The proposed research program intends to investigate the use of various risk measures in portfolio selection with behavioral considerations. The existing literature focuses on only a few classical risk measures with no attention paid to alternative risk measures especially those introduced recently. Moreover, the existing work assumes the decision-maker is rational and risk-averse, which is challenged by the theory of behavioral finance that there are systematic anomalies in human behavior that are incompatible with rationality. We plan to consider optimal investment decisions in the presence of risk constraints in which the risk is measured by various risk measures. We will allow the decision-maker to have behavioral preferences to account for human emotions and psychology. We shall also examine how various risk measures can affect financial market stability. Apart from portfolio selection, we plan to study the design of optimal reinsurance which is the most common tool for insurance companies to manage their risk exposures. The existing literature focuses on relatively simple premium principles and the optimal reinsurance strategy is typically restricted to either proportional reinsurance or excess-of-loss. The research program will consider reinsurance strategies among a general class of contracts when the reinsurance premium is calculated according to various risk measures. These are challenging problems, as only similar problems for very special cases have been studied in the literature with ad hoc methods. We will make use of the existing optimization and stochastic control techniques and develop new methods to solve the problems. This might be one of the first few attempts to systematically analyze the impacts of various risk measures on risk management decisions taking into consideration human psychology. We expect the findings of the research program will help financial managers, insurers, and regulators have a better understanding of various risk measures. In particular, the results will provide new guidance on risk management for Canadian and global financial and insurance markets. By establishing and analyzing new mathematical models, the research will contribute to optimization techniques that will be useful to other problems in mathematical finance and actuarial science. HQPs involved will develop skills in quantitative risk management necessary for a career in the financial and insurance industry, as well as in academia.

风险和不确定性是金融和保险市场不可或缺的性质。金融数学家和精算师使用风险度量来量化风险。我们使用的风险度量方法已经从定性描述发展到更定量的风险度量。大量的研究已经进行了各种风险度量的统计性质的研究，但很少知道这些风险度量如何影响金融和保险机构的风险管理决策。 建议的研究计划打算调查使用各种风险措施的投资组合选择与行为的考虑。现有的文献只关注一些经典的风险度量，而没有关注替代的风险度量，特别是最近引入的风险度量。此外，现有的研究假设决策者是理性的和风险厌恶的，这受到了行为金融理论的挑战，即人类行为中存在与理性不相容的系统性异常。我们计划考虑最优的投资决策中存在的风险约束，其中的风险是衡量各种风险措施。我们将允许决策者有行为偏好来解释人类的情感和心理。我们也将研究各种风险措施如何影响金融市场的稳定。 除了选择投资组合外，我们计划研究最佳再保险的设计，这是保险公司管理风险的最常用工具。现有的文献集中在相对简单的保费原则和最优再保险策略通常限于比例再保险或超额损失。研究计划将考虑再保险策略的一般类别的合同时，再保险保费计算根据各种风险措施。 这些都是具有挑战性的问题，因为只有非常特殊的情况下，类似的问题已经在文献中研究了特设的方法。我们将利用现有的优化和随机控制技术，并开发新的方法来解决问题。这可能是第一次尝试系统地分析各种风险措施对风险管理决策的影响，同时考虑到人类心理。我们预计，该研究项目的结果将有助于财务经理、保险公司和监管机构更好地了解各种风险措施。特别是，研究结果将为加拿大和全球金融和保险市场的风险管理提供新的指导。通过建立和分析新的数学模型，本研究将有助于优化技术，将有助于在数学金融和精算科学的其他问题。参与的HQP将培养在金融和保险行业以及学术界的职业生涯所必需的定量风险管理技能。