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Risks 2016, 4(3), 29; doi:10.3390/risks4030029

Optimal Insurance with Heterogeneous Beliefs and Disagreement about Zero-Probability Events

Imperial College Business School, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Academic Editor: Mogens Steffensen
Received: 5 May 2016 / Revised: 25 July 2016 / Accepted: 26 July 2016 / Published: 5 August 2016
View Full-Text   |   Download PDF [466 KB, uploaded 5 August 2016]

Abstract

In problems of optimal insurance design, Arrow’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’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’s probability measure, and we obtain Arrow’s classical result, as well as one of the results of Ghossoub as corollaries. Finally, we formalize Marshall’s argument that, in a setting of belief heterogeneity, an optimal indemnity schedule may take “any”shape. View Full-Text
Keywords: optimal insurance; deductible contract; subjective probability; heterogeneous beliefs; mutual singularity optimal insurance; deductible contract; subjective probability; heterogeneous beliefs; mutual singularity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ghossoub, M. Optimal Insurance with Heterogeneous Beliefs and Disagreement about Zero-Probability Events. Risks 2016, 4, 29.

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