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];