Paper: arXiv 2609.31959
Authors: Maria Andraos, Mario Ghossoub
Abstract
We consider an insurance market with hidden information, where the agent’s type is private information and is drawn from an arbitrary type space. We study implementability of a collection of retention functions, namely, how to select premium schedules so that the resulting menu of contracts is incentive compatible, or truthful. Specifically, for general type spaces, implementability is equivalent to cyclical monotonicity of the collection of retention functions. For compact interval type spaces, we show that submodularity is a sufficient condition for implementability, under suitable type ordering assumptions. Moreover, for any implementable collection of retention functions, we characterize all corresponding premium schedules, up to a common additive constant. Finally, we apply our results to several standard classes of insurance contracts, for which the general implementability conditions admit simpler characterizations, and we provide several numerical illustrations.
Complexity vs Empirical Score
- Math Complexity: 8.5/10
- Empirical Rigor: 3.0/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper presents a highly mathematical and theoretical treatment of implementability in insurance markets. While it offers novel theoretical insights, its empirical rigor is limited to numerical illustrations rather than extensive data validation or backtesting.
Research Flowchart
flowchart TD
A[Research Goal: Implementability in Insurance Markets] --> B{Key Methodology: Incentive Compatibility & Cyclical Monotonicity};
B --> C[Inputs: Arbitrary Type Space, Collection of Retention Functions];
C --> D{Computational Process: Characterize Premium Schedules};
D --> E[Key Finding 1: Cyclical Monotonicity <=> Implementability];
D --> F[Key Finding 2: Submodularity Sufficiency (Compact Interval Types)];
E & F --> G[Outcomes: Characterization of Premium Schedules, Applications to Standard Contracts];
Cited References (29)
- An Exploration in the Theory of Optimum Income Taxation (1971)
- Job Market Signaling (1973)
- Real and Complex Analysis (1987)
- I nfinite D imensional A nalysis: A H itchhiker’s G uide (2006)
- I nfinite D imensional A nalysis - $3^ rd $ edition (2006)
- A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems (2018)
- Foundations of Modern Probability (2021) — link
- A Necessary and Sufficient Condition for Rationalizability in a Quasi-Linear Context (1987)
and 21 more
- Envelope Theorems for Arbitrary Choice Sets (2002)
- Convexity and Optimization in Banach Spaces (2012)
- Uhl, JJ: Vector Measures (1977)
- Convex Analysis (1997)
- Pareto Efficient Insurance Contracts When the Insurer’s Cost Function Is Discontinuous (2003)
- The Dual Theory of Choice Under Risk (1987)
- L’extension des th 'e ories de l’ 'e quilibre 'e conomique g 'e n 'e ral et du rendement social au cas du risque (1953)
- The Market for ‘Lemons’: Quality Uncertainty and the Market Mechanism (1970)
- Pareto Optima and Competitive Equilibria with Adverse Selection and Moral Hazard (1984)
- A Dual Characterization of Incentive Efficiency (2003)
- Efficient Competitive Equilibria with Adverse Selection (2006)
- Optimal Insurance: Dual Utility, Random Losses, and Adverse Selection (2023)
- Optimal Insurance in a Monopoly: Dual Utilities with Hidden Risk Attitudes (2025) — link
- Incentive Pareto Efficiency in Monopoly Insurance Markets with Adverse Selection — → 2602.09967
- Optimal Auction Design (1981)
- Dominant Strategy Mechanisms with Multidimensional Types (2004)
- Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation (2006)
- Weak Monotonicity Suffices for Truthfulness on Convex Domains (2005)
- Extremal Incentive Compatible Transfers (2013)
- Mechanism Design without Quasilinearity (2020)
- Monotonicity and Implementability (2010)
1 of 29 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.