Social Sciences Brown Bag Seminar

We consider an optimal contracting problem in which the the agent, hired by a principal, chooses volatility components of the output process and the principal observes the output continuously, so that the principal can compute the quadratic variation of the output, but not the individual components. This leads to moral hazard with respect to the risk choices of the agent. Using a recent theory of singular changes of measures for Ito processes, we formulate the principal-agent problem in this context, and solve it in the case of CARA preferences.

In that case, the optimal contract is linear in these  factors: the contractible sources of risk, including the output, the  quadratic variation of the output and  the cross-variations between the output and the contractible risk sources.  Thus, path-dependent contracts naturally arise when there is  moral hazard with respect to risk management. We also provide comparative statics via numerical examples.