Moral Hazard in Dynamic Risk Management

We consider a contracting problem in which a principal hires an agent to manage a riskyproject. When the agent chooses volatility components of the output process and the principalobserves the output continuously, 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 ofthe agent. Using a recent theory of singular changes of measures for Ito processes, we formulatea principal-agent problem in this context, and solve it in the case of CARA preferences. In thatcase, the optimal contract is linear in these factors: the contractible sources of risk, includingthe output, the quadratic variation of the output and the cross-variations between the output andthe contractible risk sources. Thus, like sample Sharpe ratios used in practice, path-dependentcontracts naturally arise when there is moral hazard with respect to risk management. We alsoprovide comparative statics via numerical examples, showing that the optimal contract is sensitiveto the values of risk premia and the initial values of the risk exposures.nonnonouirechercheInternationa