Benxuan Shi | Searcharxiv

arXiv2026

Stackelberg Equilibria in Monopoly Insurance Markets with Probability Weighting

We study Stackelberg Equilibria (Bowley optima) in a monopolistic centralized sequential-move insurance market, with a profit-maximizing insurer who sets premia using a distortion premium principle, and a single policyholder who seeks to minimize a distortion risk measure. We show that equilibria are characterized as follows: In equilibrium, the optimal indemnity function exhibits a layer-type structure, providing full insurance over any loss layer on which the policyholder is more pessimistic than the insurer's pricing functional about tail losses; and no insurance coverage over loss layers on which the policyholder is less pessimistic than the insurer's pricing functional about tail losses. In equilibrium, the optimal pricing distortion function is determined by the policyholder's degree of risk aversion, whereby prices never exceed the policyholder's marginal willingness to insure tail losses. Moreover, we show that both the insurance coverage and the insurer's expected profit increase with the policyholder's degree of risk aversion. Additionally, and echoing recent work in the literature, we show that equilibrium contracts are Pareto efficient, but they do not induce a welfare gain to the policyholder. Conversely, any Pareto-optimal contract that leaves no welfare gain to the policyholder can be obtained as an equilibrium contract. Finally, we consider a few examples of interest that recover some existing results in the literature as special cases of our analysis.

q-fin.RM↗

arXiv2025

Optimal Insurance in a Monopoly: Dual Utilities with Hidden Risk Attitudes

We consider a monopoly insurance market with a risk-neutral profit-maximizing insurer and a consumer with Yaari Dual Utility preferences that distort the given continuous loss distribution. The insurer observes the loss distribution but not the risk attitude of the consumer, proxied by a distortion function drawn from a continuum of types. We characterize the profit-maximizing, incentive-compatible, and individually rational menus of insurance contracts, show that equilibria are separating, and provide key properties thereof. Notably, insurance coverage and premia are monotone in the level of risk aversion; the most risk-averse consumer receives full insurance $(\textit{efficiency at the top})$; the monopoly absorbs all surplus from the least-risk averse consumer; and consumers with a higher level of risk aversion induce a higher expected profit for the insurer. Under certain regularity conditions, equilibrium contracts can be characterized in terms of the marginal loss retention per type of consumer, and they consist of menus of layered deductible contracts, where each such layered structure is determined by the risk type of the consumer. In addition, we examine the effect of a fixed insurance provision cost on equilibria. We show that if the fixed cost is prohibitively high, then there will be no $\textit{ex ante}$ gains from trade. However, when trade occurs, separating equilibrium contracts always outperform pooling equilibrium contracts, and they are identical to those obtained in the absence of fixed costs, with the exception that only part of the menu is excluded. The excluded contracts are those designed for consumers with relatively lower risk aversion, who are less valuable to the insurer. Finally, we characterize incentive-efficient menus of contracts in the context of an arbitrary type space.

econ.TH↗