Econometrics, model uncertainty and risk management in actuarial applications

精算师使用模型来量化和管理保险和金融领域的风险。准确地模拟金融风险是具有挑战性的，因为金融过程表现出复杂的动态，很难用统计模型再现。在开发模型时，精算师面临着其复杂性和实现之间的权衡。我的研究计划的第一个目标是通过研究金融中的新模型结构和开发实现它们的原创方法来改善这种权衡。 模型经常被用来预测金融和经济变量。例如，精算师需要模拟金融资产的回报，以说明、定价和管理人寿保险和养老金计划中的风险。要生成逼真的投影，必须根据数据集对模型进行校准。然而，模型和数据集的选择会显著影响财务预测。为了减少使用不适当模型的风险，可以比较几个模型的输出。我的研究计划的第二个目标是开发一个对特定模型或数据集的选择不那么依赖的模拟框架。这个框架使我们能够在预测金融情景时考虑模型的不确定性。 本世纪头十年末的金融和经济危机表明，必须改进风险管理做法。例如，保险公司的可变年金业务遭受了巨大损失。可变年金是保险公司提供的一种投资工具，它将人寿保险与财务担保结合在一起。这些担保使保险公司面临不能多样化的市场风险，只能通过风险管理策略来缓解。这一策略一般建立在理论模型的基础上，有望降低保险公司的损失风险。由于风险管理战略是基于模型假设的，其在现实世界中的有效性将取决于当这些假设被违反时它能做得多好。我的研究计划的第三个目标是开发可变年金的风险管理策略，以便在存在模型不确定性的情况下有效地缓解市场风险。

Actuaries use models to quantify and manage risks in insurance and finance. Accurately modeling financial risks is challenging because financial processes exhibit complex dynamics which are difficult to reproduce with statistical models. When developing a model, actuaries face a tradeoff between its complexity and implementation. The first objective of my research program is to improve this tradeoff by investigating new model structures in finance and by developing original methods to implement them. Models are often used to project financial and economic variables. For example, actuaries need to simulate returns on financial assets to illustrate, price and manage risks in the context of life insurance and pension plans. To generate realistic projections, the model must be calibrated to a data set. However, the choice of the model and data set can significantly influence the financial projection. To reduce the risk of using an inappropriate model, the output of several models can be compared. The second objective of my research program is to develop a simulation framework that is less dependent on the choice of a specific model or data set. This framework allows us to take model uncertainty into account when projecting financial scenarios. The financial and economic world crisis of the late 2000s revealed that risk management practices must be improved. For example, insurance companies suffered large losses on their variable annuities business. Variable annuities are investment vehicles offered by insurance companies which combine a life insurance policy with financial guarantees. These guarantees expose the insurer to market risks which cannot be diversified, but only mitigated through a risk management strategy. This strategy is generally established based on a theoretical model, and is expected to reduce the risk of loss for the insurance company. Since the risk management strategy is based on model assumptions, its effectiveness in the real world will be determined by how well it can perform when these assumptions are violated. The third objective of my research program is to develop risk management strategies for variable annuities that can mitigate market risks effectively in the presence of model uncertainty.