@article {Ghossoub2017,
	title = {Arrow\&$\#$39;s Theorem of the Deducible with Heterogeneous Beliefs},
	journal = {North American Actuarial Journal},
	volume = {21},
	number = {1},
	year = {2017},
	pages = {15-35},
	abstract = {<p>In Arrow{\textquoteright}s classical problem of demand for insurance indemnity schedules, it is well-known that the optimal insurance indemnification for an insurance buyer{\textemdash}or decision maker (DM){\textemdash}is a\&nbsp;<i>deductible</i>\&nbsp;contract when the insurer is a risk-neutral Expected-Utility (EU) maximizer and when the DM is a risk-averse EU maximizer. In Arrow{\textquoteright}s framework, however, both parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. This article reexamines Arrow{\textquoteright}s problem in a setting where the DM and the insurer have different subjective beliefs. Under a requirement of compatibility between the insurer{\textquoteright}s and the DM{\textquoteright}s subjective beliefs, we show the existence and monotonicity of optimal indemnity schedules for the DM. The belief compatibility condition is shown to be a weakening of the assumption of a monotone likelihood ratio. In the latter case, we show that the optimal indemnity schedule is a variable deductible schedule, with a state-contingent deductible that depends on the state of the world only through the likelihood ratio. Arrow{\textquoteright}s classical result is then obtained as a special case.</p>},
	url = {http://www.tandfonline.com/doi/full/10.1080/10920277.2016.1192477},
	author = {M Ghossoub}
}