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Moral Hazard in Dynamic Risk Management

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  • Jakv{s}a Cvitani'c
  • Dylan Possamai
  • Nizar Touzi

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. We identify a family of admissible contracts for which the optimal agent's action is explicitly characterized, and, using the recent theory of singular changes of measures for It\^o processes, we study how restrictive this family is. In particular, in the special case of the standard Homlstr\"om-Milgrom model with fixed volatility, the family includes all possible contracts. We solve the principal-agent 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.

Suggested Citation

  • Jakv{s}a Cvitani'c & Dylan Possamai & Nizar Touzi, 2014. "Moral Hazard in Dynamic Risk Management," Papers 1406.5852, arXiv.org, revised Mar 2015.
  • Handle: RePEc:arx:papers:1406.5852
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    File URL: http://arxiv.org/pdf/1406.5852
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    References listed on IDEAS

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    1. Dylan Possamai & Guillaume Royer & Nizar Touzi, 2013. "On the Robust superhedging of measurable claims," Papers 1302.1850, arXiv.org, revised Feb 2013.
    2. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    3. Lioui, Abraham & Poncet, Patrice, 2013. "Optimal benchmarking for active portfolio managers," European Journal of Operational Research, Elsevier, vol. 226(2), pages 268-276.
    4. Cadenillas, Abel & Cvitanic, Jaksa & Zapatero, Fernando, 2007. "Optimal risk-sharing with effort and project choice," Journal of Economic Theory, Elsevier, vol. 133(1), pages 403-440, March.
    5. Jaeyoung Sung, 1995. "Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 720-743, Winter.
    6. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958, arXiv.org, revised Jun 2012.
    7. Hui Ou-Yang, 2003. "Optimal Contracts in a Continuous-Time Delegated Portfolio Management Problem," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 173-208.
    8. Neufeld, Ariel & Nutz, Marcel, 2014. "Measurability of semimartingale characteristics with respect to the probability law," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3819-3845.
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    Cited by:

    1. Julio Backhoff & Ulrich Horst, 2014. "Conditional Analysis and a Principal-Agent problem," Papers 1412.4698, arXiv.org, revised Jun 2016.

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