Abstract
We investigate a continuous dynamic model associated with a firm size term and with an external factor term, which possesses the following peculiarities: the drift term is dominated by the principal’s investment strategy and the agent’s effort; the volatility term relies on the function \(\sqrt{G^2(t)+z_t}\) in which \(G(t)\ge 0\) is a continuously bounded function and is interpreted as external factors such as external variant risks, and \(z_t\) represents the firm size. The exact optimal contracts are obtained under full information. We find that the principal’s dividends in large firms are at lower risk since the flow of dividends increases with firm size. The optimal compensation scheme for the agent and investment plan for the principal are analyzed under specific assumptions. In extremely volatile environment with large G(t), the compensation for the agent would become overly large and the optimal investment is not achievable.
Similar content being viewed by others
References
Ai, H., Li, R.: Investment and CEO compensation under limited commitment. J Financ Econ 116(3), 452–472 (2015)
Albuquerque, R., Hopenhayn, H.A.: Optimal lending contracts and firm dynamics. Rev Econ Stud 71(2), 285–315 (2004)
Biais, B., Mariotti, T., Rochet, J.C., Villeneuve, S.: Large risks, limited liability, and dynamic moral hazard. Econometrica 78(1), 73–118 (2010)
Bottazzi, G., Coad, A., Jacoby, N., Secchi, A.: Corporate growth and industrial dynamics: evidence from french manufacturing. Appl Econ 43(1), 103–116 (2011)
Chi, C.K., Choi, K.J.: The impact of firm size on dynamic incentives and investment. Rand J Econ 48(1), 147–177 (2017)
Clementi, G.L., Cooley, T., Giannatale, S.D.: A theory of firm decline. Rev Econ Dyn 13(4), 861–885 (2010)
Cvitanić, J., Possamaï, D., Touzi, N.: Dynamic programming approach to principal agent problems. Finance Stoch 22(1), 1–37 (2018)
Demarzo, P.M., Fishman, M.J., He, Z., Wang, N.: Dynamic agency and the Q theory of investment. J Finance 67(6), 2295–2340 (2012)
Greenwood, J., Hercowitz, Z., Krusell, P.: Long-run implications of investment-specific technological change. Am Econ Rev 87(3), 342–362 (1997)
He, Z.: Optimal executive compensation when firm size follows geometric brownian motion. Rev Financ Stud 22(2), 859–892 (2009)
He, Z.: A model of dynamic compensation and capital structure. J Financ Econ 100(2), 351–366 (2011)
Holmstrom, B., Milgrom, P.: Aggregation and linearity in the provision of intertemporal incentives. Econometrica 55(2), 303–328 (1987)
Hymer, S., Pashigian, P.: Firm size and rate of growth. J Polit Econ 70, 556–569 (1962)
Reichlin, P., Siconolfi, P.: Optimal debt contracts and moral hazard along the business cycle. Econ Theory 24(1), 75–109 (2004)
Sannikov, Y.: A continuous-time version of the principal-agent problem. Rev Econ Stud 75(3), 957–984 (2008)
Schattler, H., Sung, J.: The first-order approach to the continuous-time principal-agent problem with exponential utility. J Econ Theory 61(2), 331–371 (1993)
Williams, N.: On dynamic principal-agent problems in continuous time. Working Paper, University of Wisconsin- Madison (2009)
Williams, N.: A solvable continuous time dynamic principal-agent model. J Econ Theory 159, 989–1015 (2015)
Yamada, T., Watanabe, S.: On the uniqueness of solutions of stochastic differential equations. J Math Kyoto Univ 11(1), 155–167 (1971)
Acknowledgements
The authors are very grateful to the reviewers for their valuable comments, which have led to a significant improvement of the paper.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Lai, C., Li, R. & Wu, Y. Optimal compensation and investment affected by firm size and time-varying external factors. Ann Finance 16, 407–422 (2020). https://doi.org/10.1007/s10436-020-00365-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10436-020-00365-1