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Optimal Risk-Sharing and Deductables in Insurance

Author

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  • 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
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    File URL: http://hdl.handle.net/11250/163856
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    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.
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    Cited by:

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

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    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

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