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Incentive Pareto Efficiency in Monopoly Insurance Markets with Adverse Selection

Maria Andraos, Mario Ghossoub

TL;DR

The paper studies a monopolistic insurance market with a continuum of privately known risk types, where each type’s loss distribution and risk attitude are private information. It proves that any incentive-efficient (IC and IR) contract menu is optimal for a social-welfare objective $W_{\eta,\alpha}$, establishing an equivalence between incentive Pareto efficiency and welfare maximization for general concave utilities. It then specializes to Yaari's Dual Utility, deriving a semi-explicit classification of optimal menus under two type-orderings: one where higher types are more risk-averse with larger losses, and one where higher types are less risk-averse with larger losses. In both settings, the efficient menus feature monotone funding and coverage, with the highest type receiving full coverage and the lowest type yielding zero insurer surplus, i.e., efficiency at the top and surplus extraction at the bottom. The analysis provides a robust extension of existing results to broad utility classes and continuous type spaces, with implications for design of layered retention or full-coverage contracts in asymmetric information markets.

Abstract

We study a monopolistic insurance market with hidden information, where the agent's type $θ$ is private information that is unobservable to the insurer, and it is drawn from a continuum of types. The hidden type affects both the loss distribution and the risk attitude of the agent. Within this framework, we show that a menu of contracts is incentive efficient if and only if it maximizes social welfare, subject to incentive compatibility and individual rationality constraints. This equivalence holds for general concave utility functionals. In the special case of Yaari Dual Utility, we provide a semi-explicit characterization of optimal incentive-efficient menus of contracts. We do this under two different settings: (i) the first assumes that types are ordered in a way such that larger values of $θ$ correspond to more risk-averse types who face stochastically larger losses; whereas (ii) the second assumes that larger values of $θ$ correspond to less risk-averse types who face stochastically larger losses. In both settings, the structure of optimal incentive-efficient menus of contracts depends on the level of the social welfare weight. Moreover, at the optimum, higher types receive greater coverage in exchange for higher premia. Additionally, optimal menus leave the lowest type indifferent, with the insurer absorbing all surplus from the lowest type; and they exhibit efficiency at the top, that is, the highest type receives full coverage.

Incentive Pareto Efficiency in Monopoly Insurance Markets with Adverse Selection

TL;DR

The paper studies a monopolistic insurance market with a continuum of privately known risk types, where each type’s loss distribution and risk attitude are private information. It proves that any incentive-efficient (IC and IR) contract menu is optimal for a social-welfare objective , establishing an equivalence between incentive Pareto efficiency and welfare maximization for general concave utilities. It then specializes to Yaari's Dual Utility, deriving a semi-explicit classification of optimal menus under two type-orderings: one where higher types are more risk-averse with larger losses, and one where higher types are less risk-averse with larger losses. In both settings, the efficient menus feature monotone funding and coverage, with the highest type receiving full coverage and the lowest type yielding zero insurer surplus, i.e., efficiency at the top and surplus extraction at the bottom. The analysis provides a robust extension of existing results to broad utility classes and continuous type spaces, with implications for design of layered retention or full-coverage contracts in asymmetric information markets.

Abstract

We study a monopolistic insurance market with hidden information, where the agent's type is private information that is unobservable to the insurer, and it is drawn from a continuum of types. The hidden type affects both the loss distribution and the risk attitude of the agent. Within this framework, we show that a menu of contracts is incentive efficient if and only if it maximizes social welfare, subject to incentive compatibility and individual rationality constraints. This equivalence holds for general concave utility functionals. In the special case of Yaari Dual Utility, we provide a semi-explicit characterization of optimal incentive-efficient menus of contracts. We do this under two different settings: (i) the first assumes that types are ordered in a way such that larger values of correspond to more risk-averse types who face stochastically larger losses; whereas (ii) the second assumes that larger values of correspond to less risk-averse types who face stochastically larger losses. In both settings, the structure of optimal incentive-efficient menus of contracts depends on the level of the social welfare weight. Moreover, at the optimum, higher types receive greater coverage in exchange for higher premia. Additionally, optimal menus leave the lowest type indifferent, with the insurer absorbing all surplus from the lowest type; and they exhibit efficiency at the top, that is, the highest type receives full coverage.
Paper Structure (37 sections, 22 theorems, 199 equations)

This paper contains 37 sections, 22 theorems, 199 equations.

Table of Contents

  1. Introduction
  2. The Insurance Market
  3. Efficiency under asymmetric information
  4. Incentive Pareto Optimality
  5. Social Welfare Maximization
  6. Retention Functions
  7. The Case of Dual Utilities
  8. Dual Utility Framework
  9. Type Ordering under Dual Utility
  10. Solution Characterization Under Dual Utility
  11. On the Monotonicity of the Function $\theta \mapsto J_{ \theta, \eta}(l)$
  12. Properties of the Optimal Menu
  13. Special Cases of Social Weight
  14. Insurer's Welfare Maximization
  15. Agent's Welfare Maximization
  16. ...and 22 more sections

Key Result

Theorem 3.8

A menu of contracts $( I^*_{\theta} , p^*_{\theta} )_{\theta \in \Theta}$ is incentive efficient if and only if there exists a probability measure $\eta$ on the measurable space of types $(\Theta, \mathcal{B}(\Theta))$ that is equivalent to $\mu$, and some $\alpha \in (0,1]$ such that $( I^*_{\theta

Theorems & Definitions (59)

  • Definition 2.2
  • Definition 3.3
  • Definition 3.4
  • Definition 3.5
  • Theorem 3.8
  • proof
  • Remark 3.9
  • Remark 3.10
  • Remark 3.11
  • Definition 4.1
  • ...and 49 more