Forcing and duality-corrected contracts for volatility control
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 Cvitanić, Possamaï, 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 ψ 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 ψ: 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.
Related
- Volatility-Corrected Prediction Intervals: Locally Adaptive Uncertainty Quantification for Probabilistic Time-Series Forecasting
- Distributed Model Predictive Control with Connectivity-based Contracts
- Duality for Stochastic Control with non-Markovian Random Coefficients
- Continuous-Time Wasserstein Distributionally Robust Control: Limits, Duality, and Stability
- Toscani-Fourier Distance on Probability Measures: Wasserstein Control, Topological Equivalence on Model Classes, and Duality
BibTeX
@misc{chiusolo2026forcing,
title = {{Forcing and duality-corrected contracts for volatility control}},
author = {Alessandro Chiusolo and Emma Hubert and Dylan Possamaï and Nizar Touzi},
howpublished = {HAL},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.27039},
url = {https://hal.science/hal-05854172v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Forcing and duality-corrected contracts for volatility control
AU - Alessandro Chiusolo
AU - Emma Hubert
AU - Dylan Possamaï
AU - Nizar Touzi
PY - 2026
DA - 2026/11/05
PB - HAL
DO - 10.48550/arxiv.2607.27039
UR - https://hal.science/hal-05854172v1
AB - 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 Cvitanić, Possamaï, 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 ψ 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 ψ: 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.
ER -