Optimal insurance design in the presence of imperfect information

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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.