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Efficient Risk Sharing: The Last Frontier

Author

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  • John W. Pratt

    (Harvard University, Boston, Massachusetts 02163)

Abstract

When rational risk-averse agents must choose among and share monetary risks, it is known that efficient sharing is typically nonlinear, even with common beliefs. Wherever it is, the sharing rule may affect the choice, randomized choice may allow everyone to gain, and indeed a randomized choice between unacceptable risks may be acceptable. An important exception occurs if the agents' utility functions are all exponential, all logarithmic, or all the same power (HARA). Then choices should accord with a group utility function of the same form independent of the sharing rule, randomization never helps, and all efficient sharing rules are linear. This self-contained paper simplifies, refines, and completes earlier analyses, identifying all exceptions; they are the linear sharing rules that make the agents' utilities agree. Aside from HARA, this can only occur for precisely one linear sharing rule or, in periodic versions of HARA, countably many.

Suggested Citation

  • John W. Pratt, 2000. "Efficient Risk Sharing: The Last Frontier," Management Science, INFORMS, vol. 46(12), pages 1545-1553, December.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:12:p:1545-1553
    DOI: 10.1287/mnsc.46.12.1545.12075
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    References listed on IDEAS

    as
    1. Rosing, Jakob, 1970. "The Formation of Groups for Cooperative Decision Making Under Uncertainty," Econometrica, Econometric Society, vol. 38(3), pages 430-448, May.
    2. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    3. Pratt, John W & Zeckhauser, Richard J, 1989. "The Impact of Risk Sharing on Efficient Decision," Journal of Risk and Uncertainty, Springer, vol. 2(3), pages 219-234, September.
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    Cited by:

    1. Louis John Velthuis, 2007. "Effiziente Kapitalallokation in der Banksteuerung," Schmalenbach Journal of Business Research, Springer, vol. 59(57), pages 184-210, January.
    2. Donaldson, Jason Roderick & Piacentino, Giorgia, 2018. "Contracting to compete for flows," Journal of Economic Theory, Elsevier, vol. 173(C), pages 289-319.
    3. Fedorov, Semyon & Lavrutich, Maria & Hagspiel, Verena & Lerdahl, Thomas, 2022. "Risk and benefit sharing schemes in oil exploration and production," Energy Economics, Elsevier, vol. 116(C).
    4. Schosser, Josef, 2019. "Consistency between principal and agent with differing time horizons: Computing incentives under risk," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1113-1123.
    5. Marcos Singer & Patricio Donoso & Sven Widdel, 2007. "¿Premian Las Tarifas El Desempeño Del Transportista?," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 10(1), pages 21-55.

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