Pareto-optimal insurance with an upper limit on the insurer's exposure

Oma Coke; Mario Ghossoub; Michael Zhu

doi:10.1080/03461238.2023.2239533

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Pareto-optimal insurance with an upper limit on the insurer's exposure

Journal article

Peer reviewed

Pareto-optimal insurance with an upper limit on the insurer's exposure

Oma Coke, Mario Ghossoub and Michael Zhu

Scandinavian actuarial journal, Vol.2024(3), pp.227-251

03/15/2024

DOI: 10.1080/03461238.2023.2239533

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Abstract

We examine the problem of determining Pareto-optimal (PO) insurance contracts when the insurer imposes an ex ante upper limit on disbursement. The problem is similar in spirit to that of Cummins & Mahul (2004), but it extends it in two directions: first, we use the more general and more flexible class of distortion premium principles; and second, we allow for heterogeneity in beliefs between the insurer and the insured. We unify the settings of Ghossoub (2019a, 2019b), and we adapt the approaches therein to encompass the case of a policy limit. First, we show that PO contracts are those that result from a budget-constrained optimization problem for the DM. We then provide a closed-form characterization of optimal contracts. Our result is similar in spirit to that of Cummins & Mahul (2004), who show that when policy limits are introduced to Arrow's model, PO contracts are limited deductible contracts. While Ghossoub (2019a, 2019b) shows that variable deductible contracts are optimal, the results of the present paper indicate that limited variable deductible contracts are optimal when policy limits are present. We illustrate our results via numerical examples.

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Details

Title: Subtitle: Pareto-optimal insurance with an upper limit on the insurer's exposure
Creators: Oma Coke - Murex Canada Software Ltd, Toronto, ON, Canada
Mario Ghossoub - University of Waterloo
Michael Zhu - University of Waterloo
Resource Type: Journal article
Publication Details: Scandinavian actuarial journal, Vol.2024(3), pp.227-251
DOI: 10.1080/03461238.2023.2239533
ISSN: 0346-1238
eISSN: 1651-2030
Publisher: Taylor & Francis
Number of pages: 25
Grant note: 2018-03961 / Natural Sciences and Engineering Research Council of Canada; Natural Sciences and Engineering Research Council of Canada (NSERC); CGIAR
Language: English
Date published: 03/15/2024
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9985179680802771

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