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PROBABILITY SEMINAR BY JAKSA CVITANIC
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Principal-Agent Problems in Continuous Time
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Motivated by the problems of optimal compensation
of executives and of investment fund managers,
we consider principal-agent problems in continuous time,
when the principal's and the agent's risk-aversion
are modeled by standard utility
functions. The agent can control both the drift (the ``mean") and the
volatility
(the ``variance")
of the underlying stochastic process.
The principal decides what type of contract/payoff to give to the agent.
We use martingale/duality methods
familiar from the theory of
continuous-time optimal
portfolio selection.
Our results depend on whether the agent can control the drift
independently of the volatility, or not, and whether they have the same
utility functions.
We get the following results in illustrative examples
of our general theory:
if both the agent and the principal have the same
power utility,
or they both have (possibly different) exponential utilities, the optimal
contract is
(ex-post) linear;
if they have different power utilities, the optimal contract is nonlinear.
We also present an example in which a call option-type
contract is optimal.
Finally, we establish an approach for solving
the principal-agent problem in very general models and with
a general cost function, and show how the approach works
in non-trivial examples.