Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 95203, 27 pages

Optimal contracts in continuous-time models

Jakša Cvitanić,1 Xuhu Wan,2 and Jianfeng Zhang3

1Division of the Humanities and Social Sciences, Caltech, MC 228-77, 1200 E California Boulevard, Pasadena 91125, CA, USA
2Department of Information and Systems Management, HKUST Business School, Clear Water Bay, Kowloon, Hong Kong
3Department of Mathematics MC 2532, University of Southern California, 3620 S Vermont Avenue, Los Angeles 90089-1113, CA, USA

Received 17 November 2005; Revised 3 February 2006; Accepted 19 February 2006

Copyright © 2006 Jakša Cvitanić et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a unified approach to solving contracting problems with full information in models driven by Brownian motion. We apply the stochastic maximum principle to give necessary and sufficient conditions for contracts that implement the so-called first-best solution. The optimal contract is proportional to the difference between the underlying process controlled by the agent and a stochastic, state-contingent benchmark. Our methodology covers a number of frameworks considered in the existing literature. The main finance applications of this theory are optimal compensation of company executives and of portfolio managers.