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Insurance pricing with complete information, state-dependent utility, and production costs

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  • Ramsay, Colin M.
  • Oguledo, Victor I.

Abstract

We consider a group of identical risk-neutral insurers selling single-period indemnity insurance policies. The insurance market consists of individuals with common state-dependent utility function who are identical except for their known accident probability q. Insurers incur production costs (commonly called expenses or transaction costs by actuaries) that are proportional to the amount of insurance purchased and to the premium charged. By introducing the concept of insurance desirability, we prove that the existence of insurer expenses generates a pair of constants qmin and qmax that naturally partitions the applicant pool into three mutually exclusive and exhaustive groups of individuals: those individuals with accident probability q∈[0,qmin) are insurable but do not desire insurance, those individuals with accident probability q∈[qmin,qmax] are insurable and desire insurance, and those individuals with accident probability q∈(qmax,1] desire insurance but are uninsurable. We also prove that, depending on the level of q and the marginal rate of substitution between states, it may be optimal for individuals to buy complete (full) insurance, partial insurance, or no insurance at all. Finally, we prove that when q is known in monopolistic markets (i.e., markets with a single insurer), applicants may be induced to “over insure” whenever partial insurance is bought.

Suggested Citation

  • Ramsay, Colin M. & Oguledo, Victor I., 2012. "Insurance pricing with complete information, state-dependent utility, and production costs," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 462-469.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:3:p:462-469
    DOI: 10.1016/j.insmatheco.2012.02.004
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    References listed on IDEAS

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    1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    2. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Joseph E. Stiglitz, 1977. "Monopoly, Non-linear Pricing and Imperfect Information: The Insurance Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(3), pages 407-430.
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    Cited by:

    1. hector chade, 2016. "The Market for Lemons: Costly Insurance, Coverage Denials, and Pooling," 2016 Meeting Papers 1097, Society for Economic Dynamics.
    2. Ramsay, Colin M. & Oguledo, Victor I. & Pathak, Priya, 2013. "Pricing high-risk and low-risk insurance contracts with incomplete information and production costs," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 606-614.
    3. Jost, Peter-J., 2016. "Competitive insurance pricing with complete information, loss-averse utility and finitely many policies," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 11-21.
    4. Chade, Hector & Schlee, Edward E., 2020. "Insurance as a lemons market: Coverage denials and pooling," Journal of Economic Theory, Elsevier, vol. 189(C).
    5. Yann Braouezec, 2015. "Public versus Private Insurance System with (and without) Transaction Costs: Optimal Segmentation Policy of an Informed monopolistPublic versus Private Insurance System with (and without) Transaction ," Working Papers 2013-ECO-23, IESEG School of Management, revised May 2014.
    6. Kartashova Olga Ivanovna & Molchanova Olga Vladimirovna & Axana Turgaeva, 2018. "Insurance Risks Management Methodology," JRFM, MDPI, vol. 11(4), pages 1-15, October.
    7. Torraca, Ana Patrícia & Fanzeres, Bruno, 2021. "Optimal insurance contract specification in the upstream sector of the oil and gas industry," European Journal of Operational Research, Elsevier, vol. 295(2), pages 718-732.

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