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Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision

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  • Hellwig, Martin F.
  • Schmidt, Klaus M.

Abstract

This paper studies the relation between discrete-time and continuoustime principal-agent models. We derive the continuous-time model as a limit of discretetime models with ever shorter periods and show that optimal incentive schemes in the discrete-time models approximate the optimal incentive scheme in the continuous model, which is linear in accounts. Under the additional assumption that the principal observes only cumulative total profits at the end and the agent can destroy profits unnoticed, an incentive scheme that is linear in total profits is shown to be approximately optimal in the discrete-time model when the length of the period is small.

Suggested Citation

  • Hellwig, Martin F. & Schmidt, Klaus M., 2001. "Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Discussion Papers in Economics 22, University of Munich, Department of Economics.
    • Handle: RePEc:lmu:muenec:22
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    References listed on IDEAS

    as
    1. Martin F. Hellwig & Klaus M. Schmidt, 2002. "Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Econometrica, Econometric Society, vol. 70(6), pages 2225-2264, November.
    2. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    3. Hellwig, Martin F., 1996. "Sequential decisions under uncertainty and the maximum theorem," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 443-464.
    4. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    5. Itoh, Hideshi, 1992. "Cooperation in Hierarchical Organizations: An Incentive Perspective," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 8(2), pages 321-345, April.
    6. J. A. Mirrlees, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 3-21.
    7. Jaeyoung Sung, 1995. "Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 720-743, Winter.
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    More about this item

    Keywords

    Principal-agent problems ; linear incentive schemes ; intertemporal incentive provision ; Brownian motion;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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