  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.
