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Mathematics and Financial Economics

, Volume 1, Issue 1, pp 21–55 | Cite as

Optimal compensation with adverse selection and dynamic actions

  • Jakša Cvitanić
  • Jianfeng Zhang
Original Article

Abstract

We consider continuous-time models in which the agent is paid at the end of the time horizon by the principal, who does not know the agent’s type. The agent dynamically affects either the drift of the underlying output process, or its volatility. The principal’s problem reduces to a calculus of variation problem for the agent’s level of utility. The optimal ratio of marginal utilities is random, via dependence on the underlying output process. When the agent affects the drift only, in the risk- neutral case lower volatility corresponds to the more incentive optimal contract for the smaller range of agents who get rent above the reservation utility. If only the volatility is affected, the optimal contract is necessarily non-incentive, unlike in the first-best case. We also suggest a procedure for finding simple and reasonable contracts, which, however, are not necessarily optimal.

Keywords

Adverse selection Moral hazard Principal-agent problems Continuous-time models Contracts Managers compensation 

JEL Classification

C61 C73 D82 J33 M52 

Mathematics Subject Classification (2000)

91B28 93E20 

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References

  1. 1.
    Admati A.R. and Pfleiderer P. (1997). Does it all add up? Benchmarks and the compensation of active portfolio managers. J. Bus. 70: 323–350 CrossRefGoogle Scholar
  2. 2.
    Arora, N., Ou-Yang, H.: A Continuous-time model of explicit and implicit incentives. Working paper, University of North Carolina (2000)Google Scholar
  3. 3.
    Baron D. and Besanko D. (1987). Monitoring, moral hazard, asymmetric information and risk sharing in procurement contracting. Rand J. Econ. 18: 509–532 CrossRefGoogle Scholar
  4. 4.
    Baron D. and Holmstrom B. (1980). The investment banking contract for new issues under asymmetric information: delegation and the incentive problem. J. Finance 35: 1115–1138 CrossRefGoogle Scholar
  5. 5.
    Bolton P., Dewatripont M. (2005) Contract theory. MIT, CambridgeGoogle Scholar
  6. 6.
    Cadenillas A., Cvitanić J. and Zapatero F. (2007). Optimal risk-sharing with effort and project choice. J. Econ. Theory 133: 403–440 CrossRefGoogle Scholar
  7. 7.
    Cvitanić, J., Wan, X., Zhang, J.: Continuous-time principal- agent problems with hidden action and lump-sum payment. Working paper (2005)Google Scholar
  8. 8.
    Cvitanić, J., Wan, X., Zhang, J.: Optimal contracts in continuous-time models. J. Appl. Math. Stoch. Anal. (2006) Article ID 95203Google Scholar
  9. 9.
    Darrough M.N. and Stoughton N.M. (1986). Moral hazard and adverse selection: the question of financial structure. J. Finance XLI 2: 501–513 CrossRefGoogle Scholar
  10. 10.
    Davis M.H.A. and Varaiya P.P. (1973). Dynamic programming conditions for partially-observable stochastic systems. SIAM J. Control 11: 226–261 zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    DeMarzo, P., Sannikov, Y.: A Continuous-time agency model of optimal contracting and capital structure. Working paper (2004)Google Scholar
  12. 12.
    Detemple, J., Govindaraj, S., Loewenstein, M.: Hidden actions, agents with non-separable utility and wealth-robust intertemporal incentive contracts. Working paper, Boston University (2001)Google Scholar
  13. 13.
    Dybvig, P., Farnsworth, H., Carpenter, J.: Portfolio performance and agency. Working paper, Washington University in St. Louis (2001)Google Scholar
  14. 14.
    Heinkel R. and Stoughton N.M. (1994). The dynamics of portfolio management contracts. Rev. Financ. Stud. 7(2): 351–387 CrossRefGoogle Scholar
  15. 15.
    Hellwig, M., Schmidt, K.M.: Discrete-time approximations of Holmstrom- Milgrom Brownian-motion model of intertemporal incentive provision. Working paper, University of Mannheim (1998)Google Scholar
  16. 16.
    Holmstrom B. (1979). Moral hazard and observability. Bell J. Econ. 10: 74–91 CrossRefGoogle Scholar
  17. 17.
    Holmstrom B. and Milgrom P. (1987). Aggregation and linearity in the provision of intertemporal incentives. Econometrica 55: 303–328 CrossRefMathSciNetGoogle Scholar
  18. 18.
    Hugonnier, J., Kaniel, R.: Mutual fund portfolio choice in the presence of dynamic flows. Working paper, University of Lausanne (2001)Google Scholar
  19. 19.
    Kadan, O., Swinkels, J.: Moral Hazard with bounded payments. Working paper (2005a)Google Scholar
  20. 20.
    Kadan, O., Swinkels, J.: Stocks or Options? Moral Hazard, Firm Viability and the Design of Compensation Contracts. Working paper (2005b)Google Scholar
  21. 21.
    Kamien, M.I., Schwartz, N.L.: Dynamic optimization. Elsevier, Amsterdam (1991)zbMATHGoogle Scholar
  22. 22.
    Karatzas I. and Shreve S.E. (1998). Methods of mathematical finance. Springer, New York zbMATHGoogle Scholar
  23. 23.
    McAfee R.P. and McMillan J. (1986). Bidding for contracts: a principal-agent analysis. Rand J. Econ. 17: 326–338 CrossRefMathSciNetGoogle Scholar
  24. 24.
    Muller H. (1998). The first-best sharing rule in the continuous-time principal-agent problem with exponential utility. J. Econ. Theory 79: 276–280 CrossRefGoogle Scholar
  25. 25.
    Muller H. (2000). Asymptotic efficiency in dynamic principal-agent problems. J. Econ. Theory 91: 292–301 CrossRefGoogle Scholar
  26. 26.
    Ou-Yang H. (2003). Optimal contracts in a continuous-time delegated portfolio management problem. Rev. Financ. Stud. 16: 173–208 CrossRefMathSciNetGoogle Scholar
  27. 27.
    Sannikov, Y.: A Continuous-time version of the principal-agent problem. working paper, UC Berkeley (2004)Google Scholar
  28. 28.
    Schattler H. and Sung J. (1993). The first-order approach to continuous-time principal-agent problem with exponential utility. J. Econ. Theory 61: 331–371 CrossRefMathSciNetGoogle Scholar
  29. 29.
    Schattler H. and Sung J. (1997). On optimal sharing rules in discrete- and continuous- times principal-agent problems with exponential utility. J. Econ. Dyn. Control 21: 551–574 CrossRefGoogle Scholar
  30. 30.
    Sung J. (1995). Linearity with project selection and controllable diffusion rate in continuous-time principal-agent problems. Rand J. Econ. 26: 720–743 CrossRefGoogle Scholar
  31. 31.
    Sung J. (1997). Corporate insurance and managerial incentives. J. Econ. Theory 74: 297–332 zbMATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Sung J. (2005). Optimal contracts under adverse selection and moral hazard: a continuous-time approach. Rev. Financ. Stud. 18: 1021–1073 CrossRefGoogle Scholar
  33. 33.
    Williams, N.: On dynamic principal-agent problems in continuous time. Working paper, Princeton University (2004)Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Caltech, Humanities and Social SciencesPasadenaUSA
  2. 2.USC Department of MathematicsLos AngelesUSA

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