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Forcing and duality-corrected contracts for volatility control

Author

Listed:
  • Alessandro Chiusolo
  • Emma Hubert
  • Dylan Possamai
  • Nizar Touzi

Abstract

In this paper, we revisit the construction of optimal incentives in continuous-time principal-agent problems with drift and volatility control. Originally, a general approach relying on dynamic programming and second-order backward stochastic differential equations (2BSDEs) was developed by Cvitani\'c, Possama\"i, and Touzi (2018) [8] to determine the optimal form of contracts in this setting. More recently, Chiusolo and Hubert (2026) [5] proposed a BSDE-based approach by introducing an alternative `contractible-volatility' problem for the principal. In addition to the proposed new method, this work highlights that the optimality result of [8] actually hinges on an assumption, stated below as Assumption 2.3, which may not hold in general. Motivated by this, we introduce in this paper a more general class of contracts, parametrised by a function $\psi$ subject to conditions that make the contract revealing for the agent and without loss of generality for the principal. We further provide two natural specifications of $\psi$: one, inspired by the BSDE approach, yielding a forcing-type contract; the other, motivated by the 2BSDE approach, correcting the duality gap when Assumption 2.3 is not satisfied.

Suggested Citation

  • Alessandro Chiusolo & Emma Hubert & Dylan Possamai & Nizar Touzi, 2026. "Forcing and duality-corrected contracts for volatility control," Papers 2607.27039, arXiv.org.
    • Handle: RePEc:arx:papers:2607.27039
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    References listed on IDEAS

    as
    1. René Aïd & Dylan Possamaï & Nizar Touzi, 2022. "Optimal Electricity Demand Response Contracting with Responsiveness Incentives," Post-Print hal-03670395, HAL.
    2. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2018. "Dynamic programming approach to principal–agent problems," Finance and Stochastics, Springer, vol. 22(1), pages 1-37, January.
    3. Romuald Élie & Emma Hubert & Thibaut Mastrolia & Dylan Possamaï, 2021. "Mean–field moral hazard for optimal energy demand response management," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 399-473, January.
    4. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    5. René Aïd & Dylan Possamaï & Nizar Touzi, 2022. "Optimal Electricity Demand Response Contracting with Responsiveness Incentives," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 2112-2137, August.
    6. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    7. Jaeyoung Sung, 2023. "Contract Theory: Discrete- and Continuous-Time Models," Springer Books, Springer, number 978-981-99-5487-2, June.
    8. Bastien Baldacci & Dylan Possamaï, 2022. "Governmental incentives for green bonds investment," Mathematics and Financial Economics, Springer, volume 16, number 5, March.
    9. Emma Hubert & Thibaut Mastrolia & Dylan Possamai & Xavier Warin, 2020. "Incentives, lockdown, and testing: from Thucydides's analysis to the COVID-19 pandemic," Papers 2009.00484, arXiv.org, revised Apr 2022.
    10. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    11. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2017. "Moral Hazard in Dynamic Risk Management," Management Science, INFORMS, vol. 63(10), pages 3328-3346, October.
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