Optimal insurance design in the presence of imperfect information

保险是最重要的风险管理工具之一，可以对冲投保人的风险，同时也为保险公司提供了盈利的机会。在各种决策问题中，最优保险的设计几十年来一直是精算研究的前沿。过去文献中研究的无数保险模型都假设保险公司对市场有完善的了解，包括投保人的损失分配和实际损失。然而，这个假设可能并不像听起来那样正确。随着信息技术的快速发展，保险公司现在可以获得更多的客户信息，但他们的知识仍然有限，因为：第一，公司缺乏真实的损失数据；第二，客户通常不愿意报告他们的真实情况。知识的有限性或信息的不完全性不可避免地会产生逆向选择、事后道德风险和模型模糊性等问题。本文提出的研究方案旨在通过合理设计保险合同来解决上述问题。更具体地说，我和我的研究小组将：A)为具有不同风险概况的投保人设计量身定制的保险合同“菜单”；B)利用随机化机制，降低潜在的事后道德风险；C)在预期效用框架内同时设计基于实际损失和基于指数的最优补偿函数；D)在考虑模型歧义的情况下，从投保人的角度设计最优保险契约。本研究的新颖之处在于：A)考虑信息不对称和不确定性的复杂环境下的最优保险契约设计；B)在最新发展的经济框架内设计最优保险合同；C)开发更高效的顺序搜索和迭代计算算法来处理无限维优化问题。申请的资金将用于支持我研究团队的学员。每个受训者将根据研究计划分配一项任务。NSERC的资金以及其他补充资金将用于支付受训人员的工资、设备费、差旅费和其他相关费用。

Insurance is one of the most important risk management tools to hedge the risks of policyholders and meanwhile provides the insurance companies opportunities for profit. Among various decision-making problems, the design of optimal insurance has been put at the forefront of actuarial studies for decades. The myriad insurance models studied in the past literature always assume that the insurance companies have perfect knowledge of the market including the policyholders' loss distributions and their actual losses. However, this assumption may not be true as it sounds to be. With the rapid development of information technology, the insurance companies can now get access to more information of their clients, but their knowledge is still limited due to: first, the company lacks real loss data; and second, clients are often reluctant to report their real situations. The limited knowledge or imperfect information could inevitably give rise to the adverse selection, ex post moral hazard and model ambiguity issues.  This proposed research program aims to address the above issues through properly designing the insurance contract. More specifically, I and my research group are going to: A) design a "menu" of the tailored insurance contracts for policyholders with different risk profiles; B) Utilizing the randomization mechanism to reduce the potential ex post moral hazard; C) Design the optimal actual-loss-based and index-based indemnification functions simultaneously in the expected utility framework; D) design the optimal insurance contract from the policyholder's perspective when considering the model ambiguity. The novelties of this research program include: A) the design of optimal insurance contract in a more complex environment which incorporates information asymmetry and uncertainty; B) the design of optimal insurance contract within the most recently developed economic framework; C) the development of more efficient sequential search and iterative computing algorithms to deal with the infinite dimensional optimization problem. The requested funding will be used to support the trainees in my research team. Each trainee will be assigned one task as per the research proposal. The NSERC funding, as well as other complementary funding, will be used to pay the trainees' salaries, equipment fees, travel and other related expenses.