@article {Ghossoub2015b,
	title = {Optimal Insurance with Heterogeneous Beliefs and Disagreement about Zero-Probability Events},
	journal = {Risks},
	volume = {4},
	number = {3},
	year = {2016},
	pages = {29},
	abstract = {<p>In problems of optimal insurance design, Arrow{\textquoteright}s classical result on the optimality of the deductible indemnity schedule holds in a situation where the insurer is a risk-neutral Expected-Utility (EU) maximizer, the insured is a risk-averse EU-maximizer, and the two parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. Recently, Ghossoub re-examined Arrow{\textquoteright}s problem in a setting where the two parties have different subjective beliefs about the realizations of the insurable random loss, and he showed that if these beliefs satisfy a certain compatibility condition that is weaker than the Monotone Likelihood Ratio (MLR) condition, then optimal indemnity schedules exist and are nondecreasing in the loss. However, Ghossoub only gave a characterization of these optimal indemnity schedules in the special case of an MLR. In this paper, we consider the general case, allowing for disagreement about zero-probability events. We fully characterize the class of all optimal indemnity schedules that are nondecreasing in the loss, in terms of their distribution under the insured{\textquoteright}s probability measure, and we obtain Arrow{\textquoteright}s classical result, as well as one of the results of Ghossoub as corollaries. Finally, we formalize Marshall{\textquoteright}s argument that, in a setting of belief heterogeneity, an optimal indemnity schedule may take {\textquotedblleft}any{\textquotedblright}shape.</p>},
	url = {http://www.mdpi.com/2227-9091/4/3/29},
	author = {M Ghossoub}
}