Optimal Insurance with Rank-Dependent Utility and Increasing Indemnities

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).

Keywords: optimal insurance design, rank-dependent utility theory, Yaari’s dual criterion, probability weighting function, moral hazard, indemnity function, retention function, quantile formulation

JEL Classification: G22, D81, D82