Optimal risk-sharing with effort and project choice

Creators: Cadenillas, Abel; Cvitanić, Jakša; Zapatero, Fernando

Abstract

We consider first-best risk-sharing problems in which "the agent" can control both the drift (effort choice) and the volatility of the underlying process (project selection). In a model of delegated portfolio management, it is optimal to compensate the manager with an option-type payoff, where the functional form of the option is obtained as a solution to an ordinary differential equation. In the general case, the optimal contract is a fixed point of a functional that connects the agent's and the principal's maximization problems. We apply martingale/duality methods familiar from optimal consumption-investment problems.

Additional Information

© 2006 Elsevier. Received 4 May 2004; revised 14 December 2005. Available online 13 February 2006. The research of A. Cadenillas was supported by the Social Sciences and Humanities Research Council of Canada grant 410 - 2003 - 1401. The research of J. Cvitaníc was supported in part by the National Science Foundation, under Grant NSF-DMS-00-99549 and DMS 04-03575. This paper is based on a previous paper titled \Dynamic Principal-Agent Problems with Perfect Information." We are very grateful to seminar and conference participants at the Bachelier Finance Society Third World Congress (Chicago), Caltech, Carnegie- Mellon, Columbia, the June 2004 Croatian Congress of Mathematics (Split, Croatia), Princeton, UC-San Diego, UT-Austin, the June 2005 Workshop on Stochastic Modeling in Financial Mathematics (Centre de recherches mathématiques, Montreal), and two anonymous referees, for many comments and suggestions. Existing errors are our sole responsibility.

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Optimal risk-sharing with effort and project choice

Abstract

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