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Optimal Claim Settlement Strategies under Constraint of Cap on Claim Loss

Author

Listed:
  • Hong Mao

    (School of Economics and Management, Shanghai Second Polytechnic University, Shanghai 201209, China)

  • Krzysztof Ostaszewski

    (Department of of Mathematics, Illinois State University, Normal, IL 61790-4520, USA)

Abstract

In this paper, we examine the question of how to devise an optimal insurance claim settlement scheme under the constraint of a cap on the amount of the claim payment. We establish objective functions to maximize the net benefit due to exaggerated claims while at the same time maximizing the total expected wealth of the insured. Then, we establish a dual objective function to minimize the total expected loss, including the perspective of the insurer. Finally, we illustrate applications of our work and provide numerical analysis of it along with an example.

Suggested Citation

  • Hong Mao & Krzysztof Ostaszewski, 2021. "Optimal Claim Settlement Strategies under Constraint of Cap on Claim Loss," Mathematics, MDPI, vol. 9(24), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3284-:d:705057
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    References listed on IDEAS

    as
    1. Borch, Karl, 1975. "Optimal Insurance Arrangements," ASTIN Bulletin, Cambridge University Press, vol. 8(3), pages 284-290, September.
    2. Crocker, Keith J & Tennyson, Sharon, 2002. "Insurance Fraud and Optimal Claims Settlement Strategies," Journal of Law and Economics, University of Chicago Press, vol. 45(2), pages 469-507, October.
    3. Klick, Jonathan & MacDonald, John, 2020. "Deterrence and liability for intentional torts," International Review of Law and Economics, Elsevier, vol. 63(C).
    4. J. David Cummins & Olivier Mahul, 2004. "The Demand for Insurance With an Upper Limit on Coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(2), pages 253-264, June.
    5. Rachel J. Huang & Larry Y. Tzeng, 2007. "Optimal Tax Deductions for Net Losses Under Private Insurance With an Upper Limit," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(4), pages 883-893, December.
    6. J. David Cummins & Olivier Mahul, 2004. "The demand for insurance with an upper limit on coverage," Post-Print hal-01952122, HAL.
    7. Keith J. Crocker & John Morgan, 1998. "Is Honesty the Best Policy? Curtailing Insurance Fraud through Optimal Incentive Contracts," Journal of Political Economy, University of Chicago Press, vol. 106(2), pages 355-375, April.
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