On Belief Singularity and the Optimality of Deductible Indemnity Schedules

15 Pages Posted: 24 Sep 2019

Date Written: September 10, 2019

Abstract

In Ghossoub (2019), we studied a problem of optimal insurance design under belief heterogeneity. We examined the effect of the divergence in beliefs, and the singularity between the beliefs, on optimal indemnities; and we provided a closed-form characterization of optimal indemnity schedules. In this paper, we build upon the work of Ghossoub (2019) and introduce a belief singularity metric to examine the effect of the level of singularity between the beliefs on the shape of optimal indemnity schedules. Our main result shows that for any level x of belief singularity with respect to the insurer's belief Q, there exists a probability measure P exhibiting a level x of belief singularity with respect to Q, such that an optimal indemnity for a decision maker with belief P is a linear deductible with Q-probability 1, and full insurance with Q-probability 0. In this sense, we show that from the perspective of the insurer, linear deductible indemnity schedules are robust to belief singularity, which gives a possible explanation of the popularity of these contracts in practice.

Keywords: Optimal Insurance, Indemnity Function, Retention Function, Deductible, Heterogeneous Beliefs, Singularity

JEL Classification: C02, D86, G22

Suggested Citation

Ghossoub, Mario, On Belief Singularity and the Optimality of Deductible Indemnity Schedules (September 10, 2019). Available at SSRN: https://ssrn.com/abstract=3453829 or http://dx.doi.org/10.2139/ssrn.3453829

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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