Optimal Insurance under Maxmin Expected Utility

TL;DR

This paper analyzes optimal insurance indemnity design when the insured exhibits ambiguity aversion modeled by Maxmin-Expected Utility, considering belief heterogeneity, no-sabotage constraints, and ambiguity sets, providing a comprehensive framework with illustrative examples.

Contribution

It offers a unified analysis of optimal indemnity functions under ambiguity aversion, belief heterogeneity, and no-sabotage constraints, including numerical studies with ambiguity sets.

Findings

Full insurance on events with zero insurer probability is optimal under belief singularity.

No-sabotage constraints influence the structure of optimal indemnities.

Ambiguity sets affect the form and robustness of optimal insurance solutions.

Abstract

We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the Maxmin-Expected Utility model of Gilboa and Schmeidler (1989), whereas the insurer is a (risk-averse or risk-neutral) Expected-Utility maximizer. We characterize optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, marginal utility of wealth, belief heterogeneity, as well as ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how the singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several illustrative examples, and we provide numerical studies for the case of a Wasserstein and a Renyi ambiguity set.