Risk measures in portfolio selection and optimal reinsurance

风险和不确定性是金融和保险市场不可缺少的本质。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已经从定性描述演变为更定量的风险度量。对各种风险度量的统计性质进行了大量的研究，但对这些风险度量如何影响金融和保险机构的风险管理决策却知之甚少。提出的研究计划旨在调查在投资组合选择与行为考虑的各种风险措施的使用。现有的文献只关注少数经典的风险度量，而没有关注替代风险度量，特别是最近引入的替代风险度量。此外，现有的研究假设决策者是理性的、风险厌恶的，这一假设受到了行为金融学理论的挑战，即人类行为中存在与理性不相容的系统性异常。我们计划在存在风险约束的情况下考虑最优投资决策，其中风险是通过各种风险度量来衡量的。我们将允许决策者有行为偏好来解释人类的情感和心理。我们还将研究各种风险措施如何影响金融市场的稳定。除了投资组合选择外，我们还计划研究最优再保险的设计，这是保险公司管理风险暴露的最常用工具。现有文献关注相对简单的保费原则，最优再保险策略通常限于比例再保险或超额赔付。本研究计划将根据不同的风险度量来计算再保险保费时，考虑一般类型合约的再保险策略。这些都是具有挑战性的问题，因为只有在非常特殊的情况下，类似的问题才在文献中用特别的方法研究过。我们将利用现有的优化和随机控制技术，开发新的方法来解决这些问题。这可能是系统地分析各种风险措施对考虑人类心理的风险管理决策的影响的最初几次尝试之一。我们期望研究计划的结果将有助于财务经理、保险公司和监管机构更好地理解各种风险措施。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，该研究将有助于优化技术，这将有助于解决数学金融和精算科学中的其他问题。参与的hqp将发展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。

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.