Principal-Agent Problems in Insurance Design

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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.