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Moral Hazard in Dynamic Risk Management (2014)
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@MISC{̈14moralhazard,
author = {Dylan Possamaı ̈ and Nizar Touzi},
title = {Moral Hazard in Dynamic Risk Management},
year = {2014}
}
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Abstract
Abstract. We consider a contracting problem in which a principal hires an agent to manage a risky project. When the agent chooses volatility components of the output process and the principal ob-serves 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 of the agent. Using a recent theory of singular changes of measures for Ito processes, we formulate a 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 haz-ard with respect to risk management. We also provide comparative statics via numerical examples, showing that the optimal contract is sensitive to extreme values of risk premia and initial values of the risk exposures.
Keyphrases
dynamic risk management moral hazard optimal contract quadratic variation recent theory volatility component ito process principal ob-serves contractible risk source risk premia output process risky project contractible source individual component singular change risk choice risk exposure path-dependent contract comparative static cara preference principal-agent problem numerical example initial value contracting problem
