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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: sandy@ad.unc.edu
Shaler Stidham
Affiliation:
Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA. E-mail: sandy@ad.unc.edu
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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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References

Arrow, K. (1963). Uncertainty and the welfare economics of medical care. The American Economic Review 53(5): 941–973.Google Scholar
Arrow, K.J. (1965). The theory of risk aversion. Aspects of the Theory of Risk-Bearing. Lecture 2. Helsinki: Yrjö Jansson Foundation.Google Scholar
Bertsimas, D. & Sim, M. (2004). The price of robustness. Operations Research 52(1): 35–53.CrossRefGoogle Scholar
Bielecki, T.R., Jeanblanc, M., & Rutkowski, M. (2007). Hedging of basket credit derivatives in credit default swap market. Journal of Credit Risk 3: 91–132.CrossRefGoogle Scholar
Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81(3): 637–654.CrossRefGoogle Scholar
Borch, K. (1960). The safety loading of reinsurance premiums. Skandinavisk Aktuariehdskrift 43: 163–184.Google Scholar
Bühlmann, H. (1980). An economic premium principle. ASTIN Bulletin 11: 52–60.CrossRefGoogle Scholar
Bühlmann, H. (1984). The general economic premium principle. ASTIN Bulletin 14: 13–21.CrossRefGoogle Scholar
Cummins, J.D. & Trainar, P. (2009). Securitization, insurance, and reinsurance. The Journal of Risk and Insurance 76(3): 463–492.CrossRefGoogle Scholar
Embrechts, P. (2000). Actuarial versus financial pricing of insurance. The Journal of Risk Finance 1(4): 17–26.CrossRefGoogle Scholar
Embrechts, P. & Meister, S. (1997). Pricing insurance derivatives: the case of CAT-futures. Bowles Symposium on Securitization of Risk, Society of Actuaries, Working Paper M-FI97-1, pp. 15–26.Google Scholar
Esscher, F. (1932). On the probability function in the collective theory of risk. Scandinavian Actuarial Journal 15: 175–195.Google Scholar
Froot, K. (2007). Risk management, capital budgeting, and capital structure policy for insurers and reinsurers. The Journal of Risk and Insurance 74(2): 273–299.CrossRefGoogle Scholar
Hull, J. & White, A. (2001). The general Hull-White model and supercalibration. Financial Analysts Journal 57: 34–43.CrossRefGoogle Scholar
Lewis, M. (2007). In nature's casino. New York Times Magazine. http://www.nytimes.com/2007/08/26/magazine/26neworleans-t.html, August 26.Google Scholar
Pratt, J.W. (1965). Risk aversion in the small and in the large. Econometrica 32(1/2): 122–136.CrossRefGoogle Scholar
Westover, K (2014). Captives and the management of risk, 3rd ed. Dallas, TX: IMRi Publications.Google Scholar