In a continuous-time setting where a risk-averse agent controls the drift ofan output process driven by a Brownian motion, optimal contracts are linear inthe terminal output; this result is well-known in a setting with moral hazardand -under stronger assumptions - adverse selection. We show that this resultcontinues to hold when in addition reservation utilities are type-dependent.This type of problem occurs in the study of optimal compensation problemsinvolving competing principals.
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