IDEAS home Printed from https://ideas.repec.org/p/hhs/nhhfms/2006_024.html
   My bibliography  Save this paper

Optimal Risk-Sharing and Deductables in Insurance

Author

Listed:
  • Aase, Knut K.

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

Abstract

Risk-sharing in insurance is analyzed, with a view towards explaining the prevalence of deductibles. First we introduce, in a modern setting, the main concepts of the theory of risk-sharing in a group of agents. This theory we apply to the risk-sharing problem between an insurer and an insurance customer. We motivate the development through simple examples, illustrating some of the subtle points of this theory. In order to deduce deductibles endogenously, not explained in the neoclassical model, we separately introduce (i) the insurable asset as a decision variable, (ii) administrative costs, and (iii) moral hazard, and illustrate by examples.

Suggested Citation

  • Aase, Knut K., 2006. "Optimal Risk-Sharing and Deductables in Insurance," Discussion Papers 2006/24, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2006_024
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/11250/163856
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Aase, Knut K., 2007. "Wealth Effects on Demand for Insurance," Discussion Papers 2007/6, Norwegian School of Economics, Department of Business and Management Science.
    2. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    3. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Borch, Karl, 1960. "Reciprocal Reinsurance Treaties," ASTIN Bulletin, Cambridge University Press, vol. 1(4), pages 170-191, December.
    5. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    6. Bengt Holmstrom, 1979. "Moral Hazard and Observability," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 74-91, Spring.
    7. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Knut K. Aase, 1992. "Dynamic Equilibrium and the Structure of Premiums in a Reinsurance Market," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 17(2), pages 93-136, December.
    11. Baton, Bernard & Lemaire, Jean, 1981. "The Core of a Reinsurance Market," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 57-71, June.
    12. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    13. Gerber, Hans U., 1978. "Pareto-Optimal Risk Exchanges and Related Decision Problems," ASTIN Bulletin, Cambridge University Press, vol. 10(1), pages 25-33, May.
    14. Wyler, Erich, 1990. "Pareto Optimal Risk Exchanges and a System of Differential Equations: a Duality Theorem," ASTIN Bulletin, Cambridge University Press, vol. 20(1), pages 23-31, April.
    15. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Knut K. Aase, 2017. "Optimal Insurance Policies in the Presence of Costs," Risks, MDPI, vol. 5(3), pages 1-17, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    2. Knut K. Aase, 2022. "Optimal Risk Sharing in Society," Mathematics, MDPI, vol. 10(1), pages 1-31, January.
    3. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    4. Aase, Knut K., 2010. "Existence and Uniqueness of Equilibrium in a Reinsurance Syndicate," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 491-517, November.
    5. Henri Loubergé, 1998. "Risk and Insurance Economics 25 Years After," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 23(4), pages 540-567, October.
    6. Prescott, Edward C. & Rios-Rull, Jose-Victor, 1992. "Classical competitive analysis of economies with Islands," Journal of Economic Theory, Elsevier, vol. 57(1), pages 73-98.
    7. repec:dau:papers:123456789/5590 is not listed on IDEAS
    8. Besada, M. & Vazquez, C., 1999. "The generalized marginal rate of substitution," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 553-560, May.
    9. Basile, Achille & Graziano, Maria Gabriella & Papadaki, Maria & Polyrakis, Ioannis A., 2017. "Cones with semi-interior points and equilibrium," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 36-48.
    10. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    11. Tourky, Rabee, 1999. "Production equilibria in locally proper economies with unbounded and unordered consumers," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 303-315, November.
    12. Jiang, Wenjun & Ren, Jiandong & Yang, Chen & Hong, Hanping, 2019. "On optimal reinsurance treaties in cooperative game under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 173-184.
    13. Aliprantis, C. D. & Tourky, R. & Yannelis, N. C., 2000. "The Riesz-Kantorovich formula and general equilibrium theory," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 55-76, August.
    14. Marakulin, Valeri M., 1998. "Production equilibria in vector lattices with unordered preferences : an approach using finite-dimensional approximations," CEPREMAP Working Papers (Couverture Orange) 9821, CEPREMAP.
    15. Flåm, Sjur Didrik, 2002. "Full Coverage for Minor, Recurrent Losses?," Working Papers in Economics 10/02, University of Bergen, Department of Economics.
    16. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.
    17. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
    18. Sonja Brangewitz & Gaël Giraud, 2012. "Learning by Trading in Infinite Horizon Strategic Market Games with Default," Documents de travail du Centre d'Economie de la Sorbonne 12062r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2013.
    19. Fuentes, Matías N., 2011. "Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 768-776.
    20. Florenzano, Monique, 1991. "Markets with countably many periods," Economics Letters, Elsevier, vol. 36(3), pages 233-238, July.
    21. He, Wei & Sun, Yeneng, 2022. "Conditional expectation of Banach valued correspondences and economic applications," Journal of Mathematical Economics, Elsevier, vol. 101(C).

    More about this item

    Keywords

    Reinsurance Exchange; Equilibrium; Pareto Optimality; Representative Agent; Core Solution; Individual Rationality; Deductibles; Costs; Moral Hazard;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:nhhfms:2006_024. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Stein Fossen (email available below). General contact details of provider: https://edirc.repec.org/data/dfnhhno.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.