Shi, Benxuan2025-08-212025-08-212025-08-212025-07-22https://hdl.handle.net/10012/22226This thesis investigates optimal insurance design in a monopolistic market under both complete and incomplete information. The motivation stems from real-world insurance settings where insurers may either fully understand policyholders’ risk characteristics or must infer them from observable behavior. We develop theoretical frameworks to model both environments and derive analytical characterizations of optimal contracts under varying assumptions. In the first part, we analyze a classical full-information setting in which the insurer knows both the policyholder’s loss distribution and risk preferences. The policyholder is assumed to be risk-averse, modeled by an increasing and concave utility function, while the insurer is risk-neutral. In a monopolistic market, the insurer, as the sole contract provider, holds significant influence over both the structure and pricing of insurance contracts. We study the impact of contract forms—such as deductibles and coinsurance—on the insurer’s optimal pricing strategy, which we express through a \textit{loading function} drawn from a class of increasing and convex functions. A central concept introduced in this framework is the \textit{Bowley solution}, which captures the sequential nature of decision-making between the insurer and the policyholder. We relate this framework to foundational literature, particularly \cite{chan1985reinsurer}. Our analysis shows that linear loading functions (yielding expected-value premiums) are optimal under coinsurance, while piecewise linear functions (aligned with stop-loss premiums) are optimal under deductible contracts. The second part retains the full-information assumption but departs from traditional convex pricing rules. Instead, we introduce ambiguity in risk assessment by distorting the probability measure using a distortion function, reflecting subjective or behavioral risk perceptions. Symmetrically, the policyholder evaluates contracts using a distortion risk measure rather than expected utility. We retain the Bowley sequential structure but relax restrictions on the contract form, assuming only that indemnity schedules are uniformly Lipschitz continuous—an assumption that helps address moral hazard. Under this generalized framework, we find that full insurance becomes optimal when the policyholder is strictly risk-averse. If the policyholder evaluates risk using Value-at-Risk (VaR), the optimal contract becomes a policy limit contract with a sharp pricing distortion aligned with the VaR confidence level. For policyholders with inverse-S-shaped distortion functions (common in behavioral models), the optimal contract takes a deductible form, and the insurer’s distortion partially mirrors the policyholder’s up to a key threshold. These results offer insight into how non-linear transformations of risk perception shape contract design. In the third part, we consider an incomplete information setting in which the insurer cannot observe a policyholder’s risk attitude. We model heterogeneity using Yaari’s dual utility theory, parameterizing preferences via a continuum of distortion functions indexed by a type parameter $\theta$. This setup introduces adverse selection: policyholders may misreport their type to secure better terms. To address this, the insurer must design a menu of contracts—each pairing a specific indemnity schedule and premium—to ensure \textit{individual rationality} (voluntary participation) and \textit{incentive compatibility} (truthful type revelation). We formulate the insurer’s profit maximization problem subject to these constraints and apply tools from mechanism design and contract theory to characterize the optimal solution. Under suitable assumptions, we find that the optimal menu consists of layered contracts with desirable properties: the most risk-averse types receive full insurance (a property known as efficiency at the top), and both coverage and pricing increase with the degree of risk aversion. The least risk-averse type is indifferent between participating and opting out, while the insurer extracts strictly positive profit from more risk-averse individuals. We also examine how the optimal menu is affected by the introduction of a fixed participation cost. In this case, the insurer chooses to withdraw part of the menu, excluding contracts targeted at the least risk-averse individuals. Additionally, we study an alternative objective in which the insurer designs an \textit{incentive-efficient} menu—one that incorporates policyholder welfare alongside profit. We show that the layered structure remains optimal in this setting and provide a detailed characterization of the associated properties of the incentive-efficient contract menu. Overall, this thesis contributes to the theoretical foundations of insurance economics in monopolistic markets and provides insights into the design and pricing of insurance contracts under both complete and asymmetric information.enDoctoral Thesis