Pareto-Optimal Insurance Contracts With Premium Budget and Minimum Charge Constraints

Abstract

In view of the fact that minimum charge and premium budget constraints are natural economic considerations in any risk-transfer between the insurance buyer and seller, this paper revisits the optimal insurance contract design problem in terms of Pareto optimality with imposing these practical constraints. Pareto optimal insurance contracts, with indemnity schedule and premium payment, are solved in the cases when the risk preferences of the buyer and seller are given by Value-at-Risk or Tail Value-at-Risk. The effect of our constraints and the relative bargaining powers of the buyer and seller on the Pareto optimal insurance contracts are highlighted. Numerical experiments are employed to further examine these effects for some given risk preferences.

Keywords: Bargaining power, Minimum charge, Optimal insurance contract design, Pareto optimality, Premium budget, Proportional Hazard Transformation, Tail Value-at-Risk, Value-at-Risk

JEL Classification: C6, C7, G22