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\title{}
\author{Jaksa Cvitanic \\
  University of Southern California}
\date{Computational Finance Seminar, \\
  March 14}


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\begin{abstract}
  In this talk, we consider a principal-agent setting in
  continuous-time, first when both have perfect information. The agent
  can control both the drift (the "mean") and the volatility (the
  "variance") of the stochastic process the principal is interested
  in. The principal offers a "European option"-type contract to the
  agent.  We characterize the optimal contract in general diffusion
  models, and with a general cost function using two approaches. One
  approach is based on martingale/duality methods familiar from the
  theory of continuous-time optimal portfolio selection, and the other
  approach is based on the Maximum Principle of Stochastic Control and
  Forward-Backward Stochastic Differential Equations. The latter
  approach can be used also for problems with asymmetric information,
  in which the principal does not observe the agent's actions.
  
  We show in examples that if the principal and the agent have the
  same CRRA utility, or they both have (possibly different) CARA
  utilities, the optimal contract is (ex-post) linear; if they have
  different CRRA utilities, the optimal contract is nonlinear. We also
  present an example in which a call option-type contract is optimal.
\end{abstract}


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