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

  • Hellwig, Martin

    ()

    (Sonderforschungsbereich 504)

  • Schmidt, Klaus M.

    ()

    (Universität München)

This paper studies the relation between discrete-time and continuous-time principal-agent models. We derive the continuous-time model as a limit of discrete-time 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.

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Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number 01-52.

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Length: 85 pages
Date of creation: 29 Nov 2001
Date of revision:
Handle: RePEc:xrs:sfbmaa:01-52
Note: For helpful comments and discussions we are grateful to Darell Duffie, Oliver Hart, Florian Herold, Bengt Holmström, Nobuhiro Kiyotaki, Paul Milgrom, John Moore, Holger Müller, Sven Rady, Jae Sung, three anonymous referees and the editor, Drew Fudenberg. The first author gratefully acknowledges research support from the Schweizerischer Nationalfonds, the Deutsche Forschungsgemeinschaft, and the Taussig Chair at Harvard University. The second author is grateful for research support from the Deutsche Forschungsgemeinschaft through grants SCHM1196/2-1 and /4-1 and for the hospitality enjoyed at the economics department of Stanford University.Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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  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. Sanford J Grossman & Oliver D Hart, 2001. "An Analysis of the Principal-Agent Problem," Levine's Working Paper Archive 391749000000000339, David K. Levine.
  3. Bengt Holmstrom & Paul R. Milgrom, 1985. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Cowles Foundation Discussion Papers 742, Cowles Foundation for Research in Economics, Yale University.
  4. Hellwig, Martin F., 1996. "Sequential decisions under uncertainty and the maximum theorem," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 443-464.
  5. Mirrlees, J A, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 3-21, January.
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