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Moral Hazard in Dynamic Risk Management

Cvitanić, Jakša and Possamaï, Dylan and Touzi, Nizar (2017) Moral Hazard in Dynamic Risk Management. Management Science, 63 (10). pp. 3328-3346. ISSN 0025-1909. doi:10.1287/mnsc.2016.2493. https://resolver.caltech.edu/CaltechAUTHORS:20171117-085646065

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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 observes 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. To find the optimal contract, we develop a novel approach to solving principal–agent problems: first, we identify a family of admissible contracts for which the optimal agent’s action is explicitly characterized; then, we show that we do not lose on generality when finding the optimal contract inside this family, up to integrability conditions. To do this, we use the recent theory of singular changes of measures for Itô processes. We solve the problem in the case of CARA preferences and show that 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, like sample Sharpe ratios used in practice, path-dependent contracts naturally arise when there is moral hazard with respect to risk management. In a numerical example, we show that the loss of efficiency can be significant if the principal does not use the quadratic variation component of the optimal contract.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1287/mnsc.2016.2493DOIArticle
http://pubsonline.informs.org/doi/10.1287/mnsc.2016.2493PublisherArticle
https://arxiv.org/abs/1406.5852arXivDiscussion Paper
ORCID:
AuthorORCID
Cvitanić, Jakša0000-0001-6651-3552
Additional Information:© 2016 INFORMS. Received: June 22, 2014; Accepted: February 18, 2016; Published Online: July 21, 2016. This paper was accepted by Gustavo Manso, finance. Funding: This research was supported in part by the National Science Foundation [Grant DMS 10-08219].
Funders:
Funding AgencyGrant Number
NSFDMS 10-08219
Subject Keywords:principal–agent problem; moral hazard; risk-management; volatility/portfolio selection
Issue or Number:10
DOI:10.1287/mnsc.2016.2493
Record Number:CaltechAUTHORS:20171117-085646065
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171117-085646065
Official Citation:Moral Hazard in Dynamic Risk Management Jakša Cvitanić, Dylan Possamaï, and Nizar Touzi Management Science 201763:10 , 3328-3346
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83284
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Nov 2017 19:22
Last Modified:15 Nov 2021 19:56

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