Timing of Effort and Reward: Three-Sided Moral Hazard in a Continuous-Time Model
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Jun YangAuthors Info & Claims
Jun YangAuthors Info & ClaimsAbstract
This paper studies a three-sided moral hazard problem with one agent exerting up-front effort and two agents exerting ongoing effort in a continuous-time model. The agents' efforts jointly affect the probability of survival and thus the expected cash flow of the project. In the optimal contract, the timing of payments reflects the timing of effort: payments for up-front effort precede payments for ongoing effort. Several patterns are possible for the cash allocation between the two agents with ongoing effort. In one case, where the two agents face equally severe moral hazard, they share the cash flow equally at each point of time. In another case, where the two agents have different severities of moral hazard, their payments are sequential. In a more general case, the two agents with ongoing effort first receive the cash flow alternately with an increasing frequency of switches and then divide the cash flow at each point of time. This study provides a framework for understanding a broad set of business-contracting issues. The characteristics suggested in the optimal contract help us analyze the causes of business failure such as the recent debacle of mortgage-backed securities.
References
[1]
}}Admati, A. and Pfleiderer, P., "Robust financial contracting and the role of venture capitalists," J. Finance, v49, pp. 371-402, 1994.
[2]
}}Bhattacharya, S. and Lafontaine, F., "Double-sided moral hazard and the nature of share contracts," RAND J. Econom., v26, pp. 761-781, 1995.
[3]
}}Casamatta, C., "Financing and advising: Optimal contracts with venture capitalists," J. Finance, v58, pp. 2059-2086, 2003.
[4]
}}Chisholm, D., "Profit-sharing versus fixed-payment contracts: Evidence from the motion picture industry," J. Law, Econom., Organ., v13, pp. 169-201, 1997.
[5]
}}DeMarzo, P. and Fishman, M., "Optimal long-term financial contracting," Rev. Financial Stud., v20, pp. 2079-2128, 2007.
[6]
}}DeMarzo, P. and Sannikov, Y., "Optimal security design and dynamic capital structure in a continuous-time agency model," J. Finance, v61, pp. 2681-2724, 2006.
[7]
}}DeMarzo, P., Fishman, M., He, Z. and Wang, N., "Dynamic agency and the q theory of investment," 2009.
[8]
}}Dybvig, P. and Lutz, N., "Warranties, durability, and maintenance: Two-sided moral hazard in a continuous-time model," Rev. Econom. Stud., v60, pp. 575-597, 1993.
[9]
}}Edmans, A., Gabaix, X., Sadzik, T. and Sannikov, Y., "Dynamic incentive accounts," 2009.
[10]
}}Fuller, A., "Study of an optimum non-linear system," J. Electronics Control, v15, pp. 63-71, 1963.
[11]
}}Holmström, B., "Moral hazard and observability," Bell J. Econom., v10, pp. 74-91, 1979.
[12]
}}Holmström, B., "Moral hazard in teams," Bell J. Econom., v13, pp. 324-340, 1982.
[13]
}}Holmström, B. and Milgrom, P., "Aggregation and linearity in the provision of intertemporal incentives," Econometrica, v55, pp. 303-328, 1987.
[14]
}}Innes, R., "Limited liability and incentive contracting with ex-ante action choices," J. Econom. Theory, v52, pp. 45-67, 1990.
[15]
}}Lazear, E., "Why is there mandatory retirement?," J. Political Econom., v87, pp. 1261-1284, 1979.
[16]
}}Ou-Yang, H., "Optimal contracts in a continuous-time delegated portfolio management problem," Rev. Financial Stud., v16, pp. 173-208, 2003.
[17]
}}Ross, S., "The economic theory of agency: The principal's problem," Amer. Econom. Rev., v63, pp. 134-139, 1973.
[18]
}}Sannikov, Y., "A continuous-time version of the principal-agent problem," Rev. Econom. Stud., v75, pp. 957-984, 2008.
[19]
}}Schättler, H. and Sung, J., "The first-order approach to the continuous-time principal-agent problem with exponential utility," J. Econom. Theory, v61, pp. 331-371, 1993.
[20]
}}Sung, J., "Linearity with project selection and controllable diffusion rate in continuous-time principal-agent problems," RAND J. Econom., v74, pp. 297-332, 1995.
[21]
}}Weinstein, M., "Profit sharing contracts in Hollywood: Evolution and analysis," J. Legal Stud., v27, pp. 67-112, 1998.
[22]
}}Wilson, R., "The theory of syndicates," Econometrica, v36, pp. 119-132, 1968.
[23]
}}Wonham, W., "Note on a problem in optimal non-linear control," J. Electronics Control, v15, pp. 59-62, 1963.
[24]
}}Zelinkin, M. and Borisov, V., Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering, Birkhäuser, Boston, 1994.
- Timing of Effort and Reward: Three-Sided Moral Hazard in a Continuous-Time Model
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INFORMS
Linthicum, MD, United States
Publication History
Published: 01 September 2010
Accepted: 03 May 2010
Received: 26 April 2009
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