Principal-Agent Problems in Insurance Design

保险（合同）设计，包括定价和确定其他合同条款，是精算科学中一个至关重要的主题。传统上，通常从保险人的角度设计合同以实现某些业务目标，而被保险人的目标往往被忽视。由此产生的契约将导致被保险人的福利损失，而被保险人的行为反过来又可能对保险人的福利产生不利影响。因此，更有效的合同设计程序将考虑到缔约双方的目标。当被保险人有能力通过私人行为（如退保、提款）影响保险事件的结果时，这一点就变得尤为重要，这些行为是保险公司无法控制的，并且/或者拥有保险公司所不知道的隐藏信息（如风险类型、风险偏好），这两种信息在当今的保险市场中无处不在。本文的主要研究目标是通过委托代理问题来研究最优保险设计。委托代理问题是一个博弈论框架，它考虑了保险人和被保险人之间的相互作用，并在均衡状态下内生地产生保险契约。研究将在可变年金市场、二级寿险市场和一般保险市场进行。保险政策复杂的财务结构导致了一些前沿的委托代理问题，这些问题的解决将有助于随机控制理论的研究。由此产生的合同预计将减少保险合同的低效率，并更好地将理论预测与市场观察结合起来。学者和从业人员有望从深入了解保险合同中的相互作用中受益。从长期来看，均衡有望成为现代保险市场金融创新的驱动力，这可能会导致市场扩张。研究生和本科生将参与拟议的研究项目，并接受高质量的培训。在资助期间，预计将有相当数量的研究论文发表在顶级精算科学和数学金融期刊上。

Insurance (contract) design, including pricing and determining other contractual terms, is a topic of central importance in actuarial science. Conventionally, it is common to design a contract from the perspective of insurers to achieve certain business objectives, and insureds' objectives are often ignored. The resulting contracts would lead to welfare losses to insureds, whose behavior may in turn adversely affect the welfare of insurers. A more efficient contract design procedure hence would account for the objectives of both contracting parties. This becomes particularly important when insureds have the ability to affect the outcome of the insured events through private actions (e.g., surrender, withdrawal) that are not controllable by insurers and/or possess hidden information (e.g., risk type, risk preference) that is unknown to insurers, both of which are ubiquitous across today's insurance markets. The primary objective of the proposed research is to investigate optimal insurance designs through principal-agent problems, a game theoretic framework that accounts for the interactions between insurer and insured, and generates insurance contracts endogenously in equilibrium. The research will be carried out in variable annuity markets, secondary life insurance markets, and for general insurance. The complex financial structure for insurance policies will lead to cutting-edge principal-agent problems, solving which will contribute to the literature of stochastic control theory. The resulting contracts are expected to reduce inefficiencies in insurance contracting and to better align theoretic predictions with market observations. Academics and practitioners are expected to benefit from the deep insight into interactions in insurance contracting. In the long run, the equilibria are expected to serve as drivers of financial innovations in modern insurance markets, which potentially induce market expansions. Graduate students and undergraduate students will be involved in the proposed research projects and receive high-quality training. A significant number of research papers are expected to be published in top actuarial science and mathematical finance journals over the course of the grant.