Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 95203, 27 pages
doi:10.1155/JAMSA/2006/95203
Optimal contracts in continuous-time models
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.
Abstract
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.