In this talk I will first consider the classical Homlstrom-Milgrom problem in which the principal and the agent have CARA utilities, and the agent controls the drift of the output process. Then, I will present recent work on extending this model to the case
in which the agent chooses volatility components of the output process, as in delegated portfolio management. Using the recent theory of singular changes of measures for It\^o processes, one can identify a family of admissible contracts that leads to a tractable optimal solution.
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