Optimal Insurance with Rank-Dependent Utility and Increasing Indemnities

TL;DR

This paper develops a method to design optimal insurance contracts under rank-dependent utility with increasing indemnities, addressing moral hazard issues and providing explicit solutions and numerical comparisons.

Contribution

It introduces a new approach imposing increasing constraints on indemnities, characterizes optimal contracts via calculus of variations, and applies the results to RDU and Yaari's criteria.

Findings

Explicit solutions for optimal contracts under RDU.

Addresses moral hazard by imposing increasing indemnity constraints.

Numerical comparison shows improvements over previous models.

Abstract

Bernard et al. (2015) study an optimal insurance design problem where an individual's preference is of the rank-dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their contracts suffer from a problem of moral hazard for paying more compensation for a smaller loss. This paper addresses this setback by exogenously imposing the constraint that both the indemnity function and the insured's retention function be increasing with respect to the loss. We characterize the optimal solutions via calculus of variations, and then apply the result to obtain explicitly expressed contracts for problems with Yaari's dual criterion and general RDU. Finally, we use a numerical example to compare the results between ours and that of Bernard et al. (2015).