Abstract

We consider a continuous-time model of the project value process that can be observed only with noise, and we allow for the possibility that the manager in charge of the project can misrepresent the observed value. The manager is compensated by the shareholders, based on the filtering estimate of the project outcome. By means of a variational calculus methodology, novel for this kind of problem, we are able to compute in closed form the optimal pay-per-performance sensitivity of the compensation and the optimal misreporting action. We illustrate our theoretical predictions through a detailed comparative statics analysis, which indicates that the shareholders induce the manager to increase the amount of misreporting over time.

Keywords

  1. variational calculus
  2. stochastic filtering
  3. optimal compensation
  4. hidden action
  5. risk-sharing

MSC codes

  1. 91B28
  2. 91G80
  3. 93E20
  4. 49K10

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
N. Burns and S. Kedia (2006), The impact of performance-based compensation on misreporting, J. Financ. Econom., 79, pp. 35--67.
2.
A. Capponi and J. Cvitanić (2008), Credit risk modeling with misreporting and incomplete information, Internat. J. Theoret. Appl. Finance, 12, pp. 81--112.
3.
G. Carlier, I. Ekeland, and N. Touzi (2007), Optimal derivatives design for mean-variance agents under adverse selection, Math. Financ. Econ., 1, pp. 57--80.
4.
A. M. Cox and D. G. Hobson (2005), Local martingales, bubbles and option prices, Finance Stoch., 9, pp. 477--492.
5.
D. Cuoco and R. Kaniel (2011), Equilibrium prices in the presence of delegated portfolio management, J. Financ. Econom., 101, pp. 264--296.
6.
J. Cvitanić, X. Wan, and J. Zhang (2009), Optimal compensation with hidden action and lump-sum payment in a continuous-time model, Appl. Math. Optim., 59, pp. 99--146.
7.
B. Dacorogna (2008), Direct Methods in the Calculus of Variation, 2nd ed., Appl. Math. Sci. 78, Springer, New York.
8.
A. Figalli, Y. H. Kim, and R. J. McCann (2011), When is multidimensional screening a convex program?, J. Econom. Theory, 146, pp. 454--478.
9.
M. Fishman and K. Hagerty (2003), Mandatory vs. voluntary disclosure in markets with informed and uninformed customers, J. Law, Economics and Organization, 19, pp. 45--63.
10.
Y. Giat, S. T. Hackman, and A. Subramanian (2010), Investment under uncertainty, heterogeneous beliefs and agency conflicts, Rev. Financ. Stud., 23, pp. 1360--1404.
11.
L. Goukasian and X. Wan (2010), Optimal incentive contracts under relative income concerns, Math. Financ. Econ., 4, pp. 57--86.
12.
B. Holmstrom and P. Milgrom (1987), Aggregation and linearity in the provision of intertemporal incentives, Econometrica, 55, pp. 303--328.
13.
U. Horst and S. Moreno-Bromberg (2008), Risk minimization and optimal derivative design in a principal agent game, Math. Financ. Econ., 2, pp. 1--27.
14.
R. A. Jarrow, P. Protter, and K. Shimbo (2010), Asset price bubbles in incomplete markets, Math. Finance, 20, pp. 145--185.
15.
M. Jensen (2005), Agency costs of overvalued equity, Financ. Manag., 34, pp. 5--19.
16.
N. Ju and X. Wan (2012), Optimal compensation and pay-performance sensitivity in a continuous-time principal-agent model, Management Sci., 58, pp. 641--657.
17.
R. S. Liptser and A. N. Shiryaev (2000), Statistics of Random Processes II. Applications, Springer-Verlag, New York.
18.
M. Loewenstein and G. A. Willard (2000), Rational equilibrium asset-pricing bubbles in continuous trading models, J. Econom. Theory, 91, pp. 17--58.
19.
H. Ou-Yang (2005), An equilibrium model of asset pricing and moral hazard, Rev. Financ. Stud., 18, pp. 1253--1303.
20.
H. Schättler and J. Sung (1993), The first-order approach to continuous-time principal-agent problem with exponential utility, J. Econom. Theory, 61, pp. 331--371.
21.
H. Schättler and J. Sung (1997), On optimal sharing rules in discrete and continuous-times principal-agent problems with exponential utility, J. Econom. Dynam. Control, 21, pp. 551--574.

Information & Authors

Information

Published In

cover image SIAM Journal on Financial Mathematics
SIAM Journal on Financial Mathematics
Pages: 605 - 638
ISSN (online): 1945-497X

History

Submitted: 15 December 2011
Accepted: 2 August 2012
Published online: 11 October 2012

Keywords

  1. variational calculus
  2. stochastic filtering
  3. optimal compensation
  4. hidden action
  5. risk-sharing

MSC codes

  1. 91B28
  2. 91G80
  3. 93E20
  4. 49K10

Authors

Affiliations

Metrics & Citations

Metrics

Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited By

View Options

View options

PDF

View PDF

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share on social media

The SIAM Publications Library now uses SIAM Single Sign-On for individuals. If you do not have existing SIAM credentials, create your SIAM account https://my.siam.org.