Budget-Constrained Optimal Insurance with Belief Heterogeneity

27 Pages Posted: 25 Oct 2018 Last revised: 11 Feb 2019

Date Written: February 6, 2019

Abstract

We re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. For ease of comparison with the classical literature, we adopt the original setting of Arrow (1971), but allow for divergence in beliefs between the insurer and the insured; and in particular for singularity between these beliefs, that is, disagreement about zero-probability events. We do not impose the no sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. Under a consistency requirement between these beliefs that is weaker than the Monotone Likelihood Ratio (MLR) condition, we characterize the optimal indemnity and show that it has a simple two-part structure: full insurance on an event to which the insurer assigns zero probability, and a variable deductible on the complement of this event.

Keywords: Optimal Insurance, Deductible, Heterogeneous Beliefs

JEL Classification: C02, D86, G22

Suggested Citation

Ghossoub, Mario, Budget-Constrained Optimal Insurance with Belief Heterogeneity (February 6, 2019). Available at SSRN: https://ssrn.com/abstract=3230312 or http://dx.doi.org/10.2139/ssrn.3230312

Mario Ghossoub (Contact Author)

University of Waterloo ( email )

Dept. of Statistics & Actuarial Science
200 University Ave. W.
Waterloo, Ontario N2L 3G1
Canada

HOME PAGE: http://uwaterloo.ca/scholar/mghossou

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