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An adaptive strategy for offering m-out-of-n insurance policies

Published online by Cambridge University Press:  15 March 2022

George S. Fishman  and
Shaler Stidham Open the ORCID record for Shaler Stidham [Opens in a new window]
George S. Fishman
Affiliation:
Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA. E-mail: [email protected]
Shaler Stidham
Affiliation:
Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA. E-mail: [email protected]
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Abstract

A company with $n$ geographically widely dispersed sites seeks insurance that pays off if $m$ out of the $n$ sites experience rarely occurring catastrophes (e.g., earthquakes) during a year. This study describes an adaptive dynamic strategy that enables an insurance company to offer the policy with smaller loss probability than more conventional static policies induce, but at a comparable or lower premium. The strategy accomplishes this by periodically purchasing reinsurance on individual sites. Exploiting rarity, the policy induces zero loss with probability one if no more than one quake occurs during any review interval. The policy also may induce a profit if $m$ or more quakes occur in an interval if no quakes have occurred in previous intervals. The study also examines the benefit of more than one reinsurance policy per active site. The study relies on expected utility to determine indifference premiums and derives an upper bound on loss probability independent of premium.

Keywords

Catastrophe insuranceContingent claimDynamic hedgingMulti-property insuranceReinsuranceUtility theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 1 , January 2023 , pp. 106 - 134
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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