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Optimal Insurance Policies in the Presence of Costs

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  • Knut K. Aase

    (Norwegian School of Economics, 5045 Bergen, Norway)

Abstract

We reconsider costs in insurance, and suggest a new type of cost function, which we argue is a natural choice when there are relatively small, but frequent, claims. If a fixed cost is incurred each time a claim is made, we obtain a Pareto optimal deductible even if the cost function does not vary with the indemnity. The classical result says that deductibles appear if and only if costs are variable. This implies that when the claims are relatively small, it is not optimal for the insured to be compensated, since the costs outweigh the benefits and a deductible will naturally occur. When we constrain the contract to contain a cap, a non-trivial deductible is Pareto optimal regardless of the assumptions about the cost structure, which is what is known as an XL-contract.

Suggested Citation

  • Knut K. Aase, 2017. "Optimal Insurance Policies in the Presence of Costs," Risks, MDPI, vol. 5(3), pages 1-17, September.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:3:p:46-:d:111025
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    References listed on IDEAS

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    1. 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.
    2. GOLLIER, Ch., 1985. "Pareto-optimal risk sharing with fixed costs per claim," LIDAM Discussion Papers CORE 1985046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    5. Sandrine Spaeter & Patrick Roger, 1997. "The Design of Optimal Insurance Contracts: A Topological Approach," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 22(1), pages 5-19, June.
    6. Borch, Karl, 1960. "Reciprocal Reinsurance Treaties," ASTIN Bulletin, Cambridge University Press, vol. 1(4), pages 170-191, December.
    7. Blazenko, George, 1985. "The Design of an Optimal Insurance Policy: Note," American Economic Review, American Economic Association, vol. 75(1), pages 253-255, March.
    8. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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    Cited by:

    1. Asimit, Vali & Boonen, Tim J., 2018. "Insurance with multiple insurers: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 778-790.

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