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Moral Hazard in Dynamic Risk Management

Banff International Research Station for Mathematical Innovation and Discovery

We consider a contracting problem in which a principal\r\nhires an agent to manage a risky project.\r\nWhen the agent chooses volatility components of the output process\r\nand the principal observes the output continuously, the principal\r\ncan compute the quadratic variation of the output, but not the\r\nindividual components. This leads to moral hazard with respect to\r\nthe risk choices of the agent. Using a recent theory of singular changes\r\nof measures for Ito processes, we formulate a principal-agent\r\nproblem in this context, and solve it in the case of CARA preferences.\r\nIn that case, the optimal contract is linear in these factors:\r\nthe 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, showing that the optimal contract is sensitive to the values of risk premia and the initial values of the risk exposures.\r\n(Joint with N. Touzi and D. Possamai)\r\n

Mathematics; Game theory, economics, social and behavioral sciences; Probability theory and stochastic processes; Mathematical finance

video/mp4

Author affiliation: California Institute of Technology

2014-10-29

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/50933

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/